
547 F.3d 137 (2008)
Robert ROSS, on behalf of himself and all others similarly situated and Randal Wachsmuth, on behalf of himself and all others similarly situated, Plaintiffs-Appellees-Cross-Appellants,
v.
AMERICAN EXPRESS COMPANY, American Express Travel Related Services Company, and American Express Centurion Bank, Defendants-Appellants-Cross-Appellees.
Docket Nos. 06-4598-cv(L), 06-4759-cv(XAP).
United States Court of Appeals, Second Circuit.
Argued: July 10, 2008.
Decided: October 21, 2008.
*138 Merrill G. Davidoff (Ruthanne Gordon, Charles P. Goodwin, and David A. Langer on the brief) Berger & Montague, P.C., Philadelphia, PA, for Plaintiffs.
Jonathan M. Jacobson, Wilson Sonsini Goodrich & Rosati (Evan R. Chesler, Elizabeth Grayer, Cravath, Swaine & Moore LLP; Meredith Kotler, Wilson Sonsini Goodrich & Rosati on the brief) New York, NY, for Defendants.
Before: POOLER and HALL, Circuit Judges, and TRAGER, District Judge.[1]
POOLER, Circuit Judge:
Both parties have appealed from the memorandum and order, dated September 27, 2005, of the United States District Court for the Southern District of New York (Pauley, J.). In that decision, the district court considered both the defendants' motion to compel arbitration, pursuant to Section 4 of the Federal Arbitration Act ("FAA"), 9 U.S.C. § 4, and the plaintiffs' motion for class certification, pursuant to Federal Rule of Civil Procedure 23. The district court held: (1) that the plaintiffs could be compelled to arbitrate; but (2) that arbitration could not properly proceed before a trial in the district court determined that the arbitration clauses in the plaintiffs' cardholder agreements were validly created; and (3) that the plaintiffs' proposed "Injunctive Relief Class" could be certified, but that certification of a "Damages Class" would be premature. In a second memorandum and order, dated September 21, 2006, the district court denied the defendants' motion for reconsideration and reiterated its holding that the determination of the validity of the arbitration *139 clauses is properly made by the district court, not an arbitrator.
The plaintiffs appeal from the district court's holding that the defendants may avail themselves of the arbitration clauses in the cardholder agreements and compel the plaintiffs to arbitrate their claims. The defendants appeal from that portion of the district court's first memorandum and order which denies their motion to compel arbitration in favor of a trial in the district court concerning the validity of the arbitration clauses contained in the plaintiffs cardholder agreements. Our review compels us to conclude that we must grant the plaintiffs' appeal because we are convinced that the district court erred in holding that the cardholder agreements provide a sufficient contractual basis for sending this case to arbitration. Consequently, we have no need to consider the defendants' appeal.

FACTS
Because the sole issue we need reach on this appeal is the discrete legal question of whether or not the plaintiffs' claims are subject to arbitration, we need not set forth any extensive description of those claims. This action is related to In re Currency Conversion Fee Antitrust Litigation, a multi-district class action litigation also pending in the Southern District before Judge Pauley ("the MDL Action"). The plaintiffs in the MDL Action are holders of MasterCard, Visa, and Diners Club ("the Network Defendants") branded credit cards, which are issued by various prominent banks, including Chase, Citibank, and Bank of America ("the Issuing Banks"). The central allegation made by the plaintiffs in the MDL Action is that the Network Defendants and the Issuing Banks (collectively "the MDL Defendants") engaged in a conspiracy, in violation of, inter alia, the Sherman Act, 15 U.S.C. §§ 1 et seq., to fix fees charged to cardholders for credit card transactions involving foreign currency at a level well above that which would prevail in a competitive market. The plaintiffs also allege that the MDL Defendants engaged in a concerted effort to conceal the allegedly inflated foreign currency transaction fees from credit card holders. See generally In re Currency Conversion Fee Antitrust Litig., 265 F.Supp.2d 385 (S.D.N.Y.2003).
The plaintiffs in this action are also holders of MasterCard, VISA, and Diners Club credit cards. They assert claims against American Express Company and certain of its affiliated entities (collectively "Amex"). The plaintiffs' central allegation is that Amex "has actively conspired with the MDL Defendants to fix, maintain, and conceal the artificially inflated" foreign currency transaction fees alleged in the MDL Action. It is crucial to note that the plaintiffs in this action are not holders of Amex credit cards and therefore do not seek relief as purchasers of Amex products. Rather, Amex is alleged to have "joined, participated, ratified, and materially supported [the] collusive arrangement between and among the MDL Defendants" to charge artificially inflated fees on MasterCard, VISA, and Diners Club transactions involving foreign currencies.
In order to obtain their MasterCard and VISA credit cards, each plaintiff enters into a standard cardholder agreement with the Issuing Banks. Of particular import here is that the cardholder agreements include a broad arbitration clause which provides that "[a]ny dispute, claim, or controversy. . . arising out of or relating to relating to this Agreement" be settled in an arbitral, not a judicial, forum. The cardholder agreements leave no doubt that, should either party choose it, arbitration shall be the exclusive means of dispute resolution:

*140 YOU UNDERSTAND AND AGREE THAT IF EITHER YOU OR WE ELECT TO ARBITRATE A CLAIM, THIS ARBITRATION SECTION PRECLUDES YOU AND U.S. FROM HAVING A RIGHT OR OPPORTUNITY TO LITIGATE CLAIMS THROUGH COURT, OR TO PARTICIPATE OR BE REPRESENTED IN LITIGATION FILED IN COURT BY OTHERS. EXCEPT AS OTHERWISE PROVIDED ABOVE, ALL CLAIMS MUST BE RESOLVED THROUGH ARBITRATION IF YOU OR WE ELECT TO ARBITRATE.
The plaintiffs allege that the inclusion of these arbitration clauses in the cardholder agreements furthered the alleged conspiracy in violation of the antitrust laws. Specifically, they assert that Amex and the MDL Defendants held a series of meetings called for the purpose of "discuss[ing] the implementation of compulsory arbitration clauses on general purpose cardholders in an effort to impede consumer litigation, with a particular emphasis on class actions." The plaintiffs further allege that
[b]y colluding with its competitors to insert compulsory arbitration clauses in its cardholder agreements, American Express and its coconspirators intended to suppress competition and deprive their cardholders of a meaningful choice concerning the arbitration of disputes; shield themselves from potential liability arising from their illegal conduct; facilitate the conspiracies [to inflate foreign transaction fees]; and deprive their cardholders of their rights under the Truth in Lending Act and the nation's antitrust laws.
Again, there is no dispute that Amex is not a party to the cardholder agreements, nor that it has any other direct contractual relationship with the plaintiffs. We therefore do not see that Amex would dispute the plaintiffs' contention that "the only connection Amex claims to Plaintiff cardholders is its alleged antitrust conspiracy." Plaintiffs' Br. at 16. Amex nevertheless asserts that its status as an alleged co-conspirator with the entities which are indisputably parties to the cardholder agreements allows it to avail itself of the compulsory arbitration clauses in those agreements. Thus, in support of its motion to compel arbitration, Amex argued as follows:
Plaintiffs' antitrust claims against American Express in this action arise directly from the cardmember agreements that Plaintiffs signed with [the Issuing Banks]. Those agreements contain mandatory arbitration provisions. Plaintiffs should not be permitted to circumvent their obligation to arbitrate claims relating to those cardmember agreements through the device of a separate lawsuit against American Express. Because Plaintiffs' claims against American Express arise out of, and are intertwined with, the cardmember agreements, the doctrine of equitable estoppel requires Plaintiffs to arbitrate those claims, even though American Express is not a party to those agreements.
The district court agreed with this contention. Quoting JLM Indus., Inc. v. Stolt-Nielsen S.A., 387 F.3d 163, 176 (2d Cir.2004), Judge Pauley noted that "`a non-signatory to an arbitration agreement may compel a signatory to that agreement to arbitrate a dispute where a careful review. . . discloses that the issues the non-signatory is seeking to resolve in arbitration are intertwined with the agreement that the estopped party has signed.'" Ross v. American Express Co., No. 04 Civ. 5723, 2005 WL 2364969, at *4 (S.D.N.Y. Sept. 27, 2005) (internal quotation marks omitted). Relying upon Denney v. BDO Seidman, LLP, 412 F.3d 58, 70 (2d Cir. *141 2005), which was decided after oral argument had taken place on Amex's motion, Judge Pauley held that "allegations of concerted misconduct between a signatory and a non-signatory could establish a close relationship between them" sufficient to invoke the doctrine of equitable estoppel. Id. at *5. Thus, "[h]aving alleged that American Express acted in concert with [the Issuing Banks], Plaintiffs cannot now escape the consequences of those allegations by arguing that American Express and [the Issuing Banks] lack the requisite close relationship or that their Sherman Act claims against American Express are not connected to that relationship." Id. (internal quotation marks omitted).
Judge Pauley proceeded to "consider whether arbitration can be compelled in light of Plaintiff's claim that the [arbitration] clauses were imposed pursuant to an illegal antitrust conspiracy." Id. at *7. He began with the familiar rule of Prima Paint Corp. v. Flood & Conklin Mfg. Co., 388 U.S. 395, 403-04, 87 S.Ct. 1801, 18 L.Ed.2d 1270 (1967), to the effect that "[w]hen a party challenges the validity of an arbitration clause directly, `the federal court may proceed to adjudicate it.'" Id. Finding that the plaintiffs had "submitted evidence to support their claim" that the arbitration clauses were the product of an illegal antitrust conspiracy, Judge Pauley concluded that they were entitled to a trial on this issue and that Amex's motion to immediately compel arbitration therefore must be denied. Id. at *8-10. The instant appeals followed Judge Pauley's denial of Amex's motion for reconsideration of this holding. See Ross v. American Express Co., No. 04 Civ. 5723, 2006 WL 2707393 (S.D.N.Y. Sept. 21, 2006).

ANALYSIS

A. Jurisdiction.
To reiterate, although the district court ruled that Amex could potentially avail itself of the arbitration clauses contained in the cardholder agreements, it denied Amex's motion to immediately compel arbitration, brought pursuant to Section 4 of the FAA, because it further held that a trial must first be held to determine whether the arbitration clauses were validly made. Although we ordinarily have jurisdiction to review only final orders of district courts, see 28 U.S.C. § 1291, Section 16(a)(1)(B) of the FAA affords us jurisdiction to consider Amex's interlocutory appeal of the district court's denial of the motion to compel arbitration. 9 U.S.C. § 16(a)(1)(B).[2]
*142 While we plainly have jurisdiction to hear Amex's appeal, our jurisdiction over the plaintiffs' appeal is not so obvious and it would have been helpful if the plaintiffs had offered a bit more explanation in their briefs as to why their appeal can be entertained by this Court. The plaintiffs appeal from the district court's holding to the effect that Amex may potentially avail itself of the arbitration clauses in the cardholder agreements. Where, as here, "a federal appellate court reviews a district court decision on an interlocutory basis, it may not at the same time review unrelated questions that are not themselves entitled to expedited consideration." In re Methyl Tertiary Butyl Ether ("MTBE") Prods. Liab. Litig., 488 F.3d 112, 122 (2d Cir. 2007). But the plaintiffs assert (without any supporting analysis)and the defendants do not argue otherwisethat we may properly exercise jurisdiction pursuant to the principle of pendent appellate jurisdiction. That principle establishes that, if an interlocutory appeal of a district court's ruling is properly before us, we have the discretion to entertain an appeal of another ruling of the district court if "the two rulings were `inextricably intertwined' or if `review of the [latter] decision was necessary to ensure meaningful review of the [former].'" Id. (quoting Swint v. Chambers County Comm'n, 514 U.S. 35, 51, 115 S.Ct. 1203, 131 L.Ed.2d 60 (1995)); see also Golino v. New Haven, 950 F.2d 864, 868 (2d Cir.1991) ("[W]here we have jurisdiction to consider some questions on appeal, we may exercise our discretion to take pendent jurisdiction over related questions.").
That discretion is properly exercised here. Judge Pauley's holding that the plaintiffs may be compelled to arbitrate pursuant to the terms of their cardholder agreements was a necessary prerequisite for his holding that arbitration could not proceed until the district court determined whether the arbitration clauses in the cardholder agreements were validly created. The two rulings are thus certainly inextricably intertwined. As set forth below, however, we believe that Judge Pauley's initial ruling was incorrect. It would therefore be a manifest waste of the time and resources of parties, courts, and arbitrators were we to entertain only the defendants' appeal here, and leave consideration of the plaintiffs' appeal to some unspecified future date. That is, if arbitration is improper in this case, everyone is served if that determination is made now. We therefore hold that we have discretionary jurisdiction over the plaintiffs' appeal.

B. The Plaintiffs' Appeal.
We begin with two bedrock principles of arbitration law. First, we recognize that the FAA was "enacted to replace judicial indisposition to arbitration," Hall Street Assocs., L.L.C. v. Mattel, Inc., ___ U.S. ___, 128 S.Ct. 1396, 1402, 170 L.Ed.2d 254 (2008), and is an expression of "a strong federal policy favoring arbitration as an alternative means of dispute resolution." Hartford Accident & Indem. Co. v. Swiss Reinsurance Am. Corp., 246 F.3d 219, 226 (2d Cir.2001). In fact, this Court has said that "it is difficult to overstate the strong federal policy in favor of arbitration, and it is a policy we have often and emphatically applied." Arciniaga v. General Motors Corp., 460 F.3d 231, 234 (2d Cir.2006) (internal quotation marks omitted).
On the other hand, however, we must remember that

*143 it remains the case that arbitration "is a matter of consent, not coercion." Volt Info. Scis. v. Bd. of Trs. of Leland Stanford Junior Univ., 489 U.S. 468, 479, 109 S.Ct. 1248, 103 L.Ed.2d 488 (1989). Specifically, "`arbitration is a matter of contract,'" and therefore "`a party cannot be required to submit to arbitration any dispute which [it] has not agreed so to submit,'" Vera v. Saks & Co., 335 F.3d 109, 116 (2d Cir.2003) (quoting Transit Mix Concrete Corp. v. Local Union No. 282, 809 F.2d 963, 967 (2d Cir.1987)). Thus, "[w]hile the FAA expresses a strong federal policy in favor of arbitration, the purpose of Congress in enacting the FAA `was to make arbitration agreements as enforceable as other contracts, but not more so.'" Cap Gemini Ernst & Young, U.S., L.L.C. v. Nackel, 346 F.3d 360, 364 (2d Cir.2003) (quoting Opals on Ice Lingerie v. Bodylines Inc., 320 F.3d 362, 369 (2d Cir. 2003); further internal quotation omitted).
JLM Industries, Inc., 387 F.3d at 171.
It is obvious that this latter principle renders problematic any holding that the plaintiffs can be compelled to arbitrate with Amex. Arbitration is a matter of contract, but the plaintiffs have not entered into any contract whatever with Amex, let alone any contract containing an arbitration clause. The cardholder agreements signed by the plaintiffs, which contain the arbitration clause of which Amex seeks to avail itself, were not signed by Amex. Nevertheless, this Court has "recognized a number of common law principles of contract law that may allow non-signatories to enforce an arbitration agreement, including equitable estoppel," Ross, 478 F.3d at 99, the principle upon which the district court relied in holding that the plaintiffs could be compelled to arbitrate with Amex.[3]
The district court's opinion improperly extends the principle of compelling arbitration through equitable estoppel to a situation where the requisite contractual basis for arbitration does not exist. We therefore must reverse the district court's holding which accepts Amex's contention that it may avail itself of the arbitration clauses contained in the plaintiffs' cardholder agreements.
To begin, this Court set forth the basic doctrine in JLM Industries:
Our cases have recognized that under principles of estoppel, a non-signatory to an arbitration agreement may compel a signatory to that agreement to arbitrate a dispute where a careful review of "the relationship among the parties, the contracts they signed . . . , and the issues that had arisen among them discloses that `the issues the non-signatory is seeking to resolve in arbitration are intertwined with the agreement that the estopped party has signed.'" Choctaw Generation Ltd. P'ship v. American Home Assurance Co., 271 F.3d 403, 406 (2d Cir.2001) (internal quotation marks and citation omitted).
*144 387 F.3d at 177. In a very recent opinion, in a passage which is highly relevant to the case now before us, we elaborated upon the proper utilization of the principle of estoppel in the arbitration context:

JLM Industries did not say or mean that whenever a relationship of any kind may be found among the parties to a dispute and their dispute deals with the subject matter of an arbitration contract made by one of them, that party will be estopped from refusing to arbitrate. . . . [I]n addition to the "intertwined" factual issues, there must be a relationship among the parties of a nature that justifies a conclusion that the party which agreed to arbitrate with another entity should be estopped from denying an obligation to arbitrate a similar dispute with the adversary which is not a party to the arbitration agreement.
Sokol Holdings, Inc. v. BMB Munai, Inc., 542 F.3d 354, 359 (2d. Cir.2008).
It is also noted in JLM Industries that this Court "ha[s] had no occasion to specify the minimum quantum of `intertwinedness' required to support a finding of estoppel" and that "the estoppel inquiry is fact-specific." 387 F.3d at 178. But this Court's cases which have applied estoppel against a party seeking to avoid arbitration have tended to share a common feature in that the non-signatory party asserting estoppel has had some sort of corporate relationship to a signatory party; that is, this Court has applied estoppel in cases involving subsidiaries, affiliates, agents, and other related business entities. See Contec Corp. v. Remote Solution Co., Ltd., 398 F.3d 205, 209 (2d Cir.2005) (holding that post-merger survivor corporation could invoke arbitration agreement signed by corporation subsumed in merger); JLM Industries, 387 F.3d at 178 (holding that plaintiffs could not avoid arbitration of antitrust conspiracy claim where plaintiffs argued that the conspiratorial conduct giving rise to claim was undertaken by non-signatory parent companies rather than contracting subsidiaries); Astra Oil Co., Inc., 344 F.3d at 280 (compelling arbitration where plaintiff acted toward non-signatory affiliated corporation "as if it were signatory"); Smith/Enron Cogeneration Ltd. P'ship v. Smith Cogeneration Int'l., Inc., 198 F.3d 88, 97 (2d Cir.1999) (compelling plaintiff to arbitration where "it treated a group of related companies as though they were interchangeable").
A number of cases from the district courts of our Circuit have similarly held that estoppel is warranted when a non-signatory defendant owns or controls a signatory defendant. Most interestingly, Judge Pauley has held in the MDL Action that the Issuing Banks can avail themselves of the arbitration clauses contained in cardholder agreements signed by the Network Defendants and the plaintiffs in the MDL Action. This was because the plaintiffs had asserted the existence of "[m]ore than simply an agency relationship" between the Network Defendants and the Issuing Banks; they had in fact alleged that "the issuing banks control the network defendants." In re Currency Conversion Fee Antitrust Litig., 361 F.Supp.2d 237, 262 (S.D.N.Y.2005). See also, e.g., Birmingham Assocs., Ltd. v. Abbott Labs., 547 F.Supp.2d 295, 304 (S.D.N.Y.2008) (because non-signatory-parent company "was directly involved in negotiating" contract containing arbitration clause and "participated" in drug development program established by that contract, signatory plaintiff "could have foreseen . . . it might be required to arbitrate" with parent company); Carroll v. LeBoeuf, Lamb, Greene & McCrae, 374 F.Supp.2d 375, 378 (S.D.N.Y.2005) (because signatory plaintiffs "specifically and *145 repeatedly allege" that signatory defendant "acted at all relevant times [as] the agent" of non-signatory defendants, plaintiffs were estopped from avoiding arbitration with non-signatories); Fraternity Fund Ltd. v. Beacon Hill Asset Mgmt. LLC, 371 F.Supp.2d 571, 578 (S.D.N.Y. 2005) (non-signatory to partnership agreement could avail itself of arbitration clause contained therein where plaintiffs alleged it owned 99% of signatory).
We have also extended estoppel beyond situations involving affiliated corporate entities. Thus, this Court has applied estoppel in a situation where a defendant, while a non-signatory to the construction contract containing an arbitration clause, was nevertheless explicitly named therein as having certain tasks to perform under that contract. See Choctaw Generation Ltd. P'ship, 271 F.3d at 406 (non-signatory party which was to provide letter of credit under construction contract could avail itself of arbitration clause because "dispute concerns the duty to replenish a letter of credit"). Somewhat similarly, one of this Circuit's district courts has recently held that an employee plaintiff who signed an employment contract with one firm ("AVI") could be compelled to arbitrate her sexual harassment claims against another firm ("ESPN") under that contract because "she was hired by AVI specifically to work as a makeup artist for ESPN; . . . she was required to . . . follow the instructions and directives of ESPN talent and ESPN supervisors ...;" and she alleged that she had been harassed by ESPN employees. Ragone v. Atlantic Video at Manhattan Center, No. 07 Civ. 6084, 2008 WL 4058480, at *9 (S.D.N.Y. Aug. 29, 2008) (internal quotation marks omitted).
But the limits of the application of estoppel in compelling arbitration are well illustrated in our decision in Sokol Holdings, Inc. In that case, plaintiff Sokol entered into an energy exploration contract containing an arbitration clause ("the Emir Contract") with Tolmakov, who was the principal owner of a firm called Emir Oil LLP. The Emir Contract provided that Sokol would purchase a percentage of Tolmakov's interest in Emir Oil LLP. But Sokol alleged in its complaint that "the BMB defendants tortiously interfered with Sokol's contract rights with Tolmakov under the Emir Contract and induced Tolmakov to sell his interest in Emir to BMB instead of Sokol." 542 F.3d, at 357. BMB, which was not a party to the Emir Contract, nevertheless asserted that it was entitled under the principle of estoppel to compel Sokol to arbitrate its claims against BMB. We rejected that assertion because Sokol's complaint alleged that BMB's only relationship to the Emir Contract was as a third-party wrongdoer and, recognizing that arbitration is a matter of consent, we concluded that Sokol "in no way consented to extend [the Emir Contract] to an entity which tortiously subverted [its] rights under [the Emir Contract]." Id. 542 F.3d at 362. We supported this conclusion by a review of the cases in which this Court had applied estoppel principle to compel arbitration. That review disclosed
a pattern which is consistent with the basic principle that one does not give up one's right to court adjudication except by consent. In each case, the promise to arbitrate by [one signatory], the entity opposing arbitration, was reasonably seen on the basis of the relationships among the parties as extending not only to [the other signatory], but also to [a non-signatory related to the latter], an entity that was, or would predictably become, with [the] knowledge and consent [of the party opposing arbitration], affiliated or associated with [the other signatory] in such a manner as to make it unfair to allow [the party opposing arbitration] to avoid its commitment to *146 arbitrate on the ground that [the non-signatory] was not the very entity with which [the party opposing arbitration] had a contract. . . . It was, of course, essential in all of these cases that the subject matter of the dispute was intertwined with the contract providing for arbitration. . . . While the arbitrability of the subject matter of the dispute was an essential condition to a finding of estoppel, however, it was not sufficient to justify that conclusion. As we implied in JLM Industries in requiring a "careful review of the relationship among the parties," the further necessary circumstance was a relationship among the parties which either supported the conclusion that [the party opposing arbitration] had consented to extend its agreement to arbitrate to [the non-signatory], or, otherwise put, made it inequitable for [the party opposing arbitration] to refuse to arbitrate on the ground that it had made no agreement with [the non-signatory].
Id. (citation omitted; emphasis supplied).
This reasoning controls here. It is indisputable that the subject matter of the dispute between the partiesthe alleged conspiracy between Amex and the Issuing Banks to violate the antitrust lawsis related to the subject matter of the cardholder agreements the plaintiffs signed with the Issuing Banks. After all, the goal of the alleged conspiracy was to fix fees on transactions with foreign enterprises which the plaintiffs conducted by means of the credit cards they received as a result of signing the cardholder agreements. But the further necessary circumstance of some relation between Amex and the plaintiffs sufficient to demonstrate that the plaintiffs intended to arbitrate this dispute with Amex is utterly lacking here. Amex has no corporate affiliation with the Issuing Banks; the plaintiffs allege without contradiction that Amex is in fact a competitor of the Issuing Banks in the credit card market. Amex did not sign the cardholder agreements, it is not mentioned therein, and it had no role in their formation or performance. The plaintiffs did not in any way treat Amex as a party to the cardholder agreements. On the contrary, they do not allege to have treated Amex at all. Just as with BMB in Sokol Holdings, Inc., Amex's only relation with respect to the cardholder agreements was as a third party allegedly attempting to subvert the integrity of the cardholder agreements. In sum, arbitration is a matter of contract and, contractually speaking, the plaintiffs do not know Amex from Adam. Amex therefore cannot avail itself of the arbitration agreements contained in the cardholder agreements.
It remains for us to consider Denney v. BDO Seidman, LLP, 412 F.3d 58 (2d Cir. 2005), the case upon which Judge Pauley primarily relied in holding that the plaintiffs here could be estopped from avoiding arbitration of their claims against Amex. Denney concerned the following dispute:
Plaintiffs claim that they were recruited by accounting firms BDO, Pasquale & Bowers, LLP, and Dermody, Burke, and Brown, Certified Public Accountants, in 1999 to participate in a tax scheme, Currency Options Bring Reward Alternatives ("COBRA"). At that time, plaintiffs were expecting to realize substantial capital gains from certain stock holdings. Defendants told plaintiffs that they could offset such gains, and thereby reduce their taxes, by forming partnerships to engage in digital foreign currency option transactions. Defendants assured plaintiffs that COBRA was a lawful tax strategy and that they had an independent opinion letter from Jenkens & Gilchrist, a major law firm, attesting to COBRA's validity.
Id. at 61 (citations and footnote omitted).
The plaintiffs signed consulting agreements with the accounting firms which *147 contained broad arbitration clauses. The district court held, however, that the "`extraordinarily vague language' of the consulting agreements" rendered them "`mutually fraudulent' and consequently unenforceable. Accordingly, the district court denied defendants' motion to compel arbitration." Id. at 63 (internal citation omitted). This Court reversed that holding, finding that "[t]he district court's legal conclusion . . . fails to take into account controlling law in this Circuit, which indicates that where an arbitration provision is severable from the contract in which it is embedded, arbitration provisions may indeed be enforceable even if aspects of the underlying agreements are not." Id. at 65.
Having held that the arbitration clause in the consulting agreement was enforceable, this Court then proceeded to consider an issue which the district court had no occasion to address: whether defendant Deutsche Bank, which did not sign the consulting agreements, could avail itself of the arbitration clause in the agreements. Citing cases from the Fifth and Eleventh Circuits, this Court held that because the plaintiffs alleged that Deutsche Bank had engaged in a conspiracy relating to the COBRA tax shelters, they "cannot now escape the consequences of those allegations by arguing that the Deutsche Bank and BDO defendants . . . are not connected to Deutsche Bank's relationship with BDO." Id. at 70.
But Denney does not end at this point. Having found that conspiracy allegations were sufficient to support the possibility of the application of estoppel, this Court then "remand[ed] the cause to the district court to enable it to consider the merits of the estoppel claim asserted by the Deutsche Bank defendants and, specifically, whether the issues the Deutsche Bank defendants seek to arbitrate are indeed intertwined with the consulting agreements." Id. Upon examining what transpired on remand, we find ourselves compelled to disagree with Amex's assertion that Denney "compels affirmance here." Amex Reply Br. at 10.[4]
On remand, Judge Scheindlin examined Deutsche Bank's alleged role in the conspiracy involving the COBRA tax shelters. She found that its role was not insubstantial: "Plaintiffs opened accounts with Deutsche Bank at the recommendation of Jenkins. Deutsche Bank promoted the strategy, counseled plaintiffs, and carried out . . . securities transactions on plaintiffs' behalf." Denney v. Jenkens & Gilchrist, 412 F.Supp.2d 293, 296 (S.D.N.Y. 2005). But Judge Scheindlin still found that the plaintiffs' claims against Deutsche Bank did not arise from the consulting agreements themselves:
Plaintiffs do not allege that Deutsche Bank induced the [consulting agreements]. Deutsche Bank's alleged role in the conspiracy was to advise plaintiffs on the "nature, structure and potential financial returns" of the COBRA transactions and execute those transactions for plaintiffs. Plaintiffs allege that "the Deutsche Defendants had only limited contact with the Plaintiffs and Class Members, largely consisting of whatever conversations were necessary to get the forms completed and the money wired to *148 the Deutsche Defendants, as fiduciaries for the Plaintiffs. . . ."
Id. at 299-300 (footnotes omitted). In sum, Deutsche Bank could not avail itself of the arbitration clauses in the consulting agreements merely because it performed certain functions under the terms of the consulting agreements. On the contrary, "[i]t is not sufficient that the dispute between plaintiffs and Deutsche Bank is related to consulting services provided by BDO pursuant to the [consulting agreements]." Id. at 300.
This Court stated in JLM Industries that it would be wrong "to suggest that a claim against a co-conspirator of a party alleged to have engaged in antitrust violations will always be intertwined to a degree sufficient to work an estoppel." 387 F.3d at 178 n. 7. Judge Scheindlin's opinion on remand in Denney recognizes the vitality of the principle that the application of estoppel in the context of conspiracy allegations is problematic. It is problematic because arbitration is of course a matter of contract "under general principles of contract law" parties should not be compelled to arbitrate unless "the totality of the evidence supports an objective intention to agree to arbitrate." Sarhank Group v. Oracle Corp., 404 F.3d 657, 662 (2d Cir.2005).
The logic of Judge Scheindlin's opinion on remand in Denney applies a fortiori in the instant case. The plaintiffs here entered into cardholder agreements with the Issuing Banks in order to become holders of MasterCard, Visa, and Diners Club credit cards. As we have already noted, the plaintiffs do not allege that they have subsequently had any contact whatsoever with Amex, and the latter makes no claim to the contrary. Amex is a complete stranger to the plaintiffs' cardholder agreements; it did not sign them, it is not mentioned in them, and it performs no function whatsoever relating to their operation.
In sum, we believe that the plaintiffs have it precisely correct when they assert that "there [was] no reason for someone signing up for a Chase Visa card, for example, to believe that he (or she) was entering into any kind of relationship with [Amex]. Indeed, [Amex] was ostensibly competing against the issuing banks and their Visa and MasterCard brands/networks, in a supposedly bitter marketplace rivalry." Plaintiffs' Br. at 27. In decisive contrast to JLM Industries, where this Court applied the doctrine of equitable estoppel to alleged co-conspirators who were also the parent corporations of signatories of the arbitration agreements, and from whom the plaintiffs "purchas[ed] shipping services directly," 387 F.3d at 178, the district court here "based its findings exclusively on allegations of collusion. Such interaction has no resemblance to the conduct of the parties in this Court's equitable estoppel cases." Plaintiffs' Br. at 28 (emphasis added). We therefore reverse the district court's holding that the plaintiffs may be compelled to arbitrate with Amex based upon the principle of equitable estoppel.

C. Amex's Appeal.
Having concluded that the plaintiffs may not properly be compelled to arbitrate with Amex on the basis of their cardholder agreements, Amex's appeal of the district court's decision to the effect that arbitration could not proceed before a trial on the question of whether the arbitration clauses in the cardholder agreements were validly created is moot.

CONCLUSION
The plaintiffs' appeal is GRANTED and Amex's appeal is DENIED as moot. We REMAND this action to the district court *149 for further proceedings in conformance with this opinion.
NOTES
[1]  The Hon. David G. Trager, United States District Judge for the Eastern District of New York, sitting by designation.
[2]  This Court previously denied the plaintiffs' motion to dismiss Amex's appeal. That motion rested upon the correct assertion that Section 16 of the FAA affords the Court jurisdiction to hear interlocutory appeals from denials of motions to compel arbitration brought pursuant to Section 4 of the FAA. Section 4 provides that "[a] party aggrieved by the alleged failure, neglect, or refusal of another to arbitrate under a written agreement for arbitration may petition any United States district court . . . for an order directing that such arbitration proceed in the manner provided for in such agreement." 9 U.S.C. § 4 (emphasis added). In their motion to dismiss, the plaintiffs argued that because Judge Pauley did not find that a written agreement to arbitrate existed between the plaintiffs and Amex, but held that arbitration could be compelled pursuant to the principle of equitable estoppel, this Court could not properly hear Amex's appeal under Section 16. We rejected this argument, holding that "[i]n every relevant sense, . . . [Amex is] appealing from the refusal to compel arbitration under a written arbitration agreement." Ross v. American Express Co., 478 F.3d 96, 99 (2d Cir.2007). We note, however, that one of our sister circuits has rejected our analysis and held that an interlocutory appeal may not be taken from a denial of a motion to compel arbitration when the party bringing the appeal is not a signatory of the arbitration agreement at issue. See Carlisle v. Curtis, Mallet-Prevost, Colt & Mosle, LLP, 521 F.3d 597, 602 (6th Cir.2008). In fact, it appears that a substantial split among the Circuits has now developed over this jurisdictional question. See Sourcing Unlimited, Inc. v. Asimco Intern., Inc., 526 F.3d 38, 44 n. 6 (1st Cir. 2008).
[3]  We have held that, in addition to estoppel, the common law principles of incorporation by reference, assumption, agency, and veil-piercing/alter ego may be utilized when a signatory moves to compel arbitration with a non-signatory to a contract containing an arbitration agreement. See Merrill Lynch Inv. Managers v. Optibase, Ltd., 337 F.3d 125, 129 (2d Cir.2003). Where, however, as here, a non-signatory moves to compel arbitration with a signatory, it remains an open question in this Circuit whether the non-signatory may proceed upon any theory other than estoppel. See Astra Oil Co., Inc. v. Rover Navigation, Ltd., 344 F.3d 276, 279 n. 2 (2d Cir.2003). We do not see that Amex is seeking to compel arbitration on any other theory than estoppel, nor did the district court suggest that any theory other than estoppel was applicable here.
[4]  We hasten to point out that the remand decision in Denney appeared after Judge Pauley's decision holding that Amex could avail itself of the arbitration clauses in the cardholder agreements. It is therefore perfectly understandable that he did not consider that decision. What is not perfectly understandable is why both parties, whose briefs relating to the instant appeals were filed long after the remand decision in Denney, fail to make any mention of the decision beyond noting that this Court ordered a remand.
