POSNER, Circuit Judge.

This appeal requires us to consider the enforceability of a forum selection clause by entities not named as parties to the contract in which the clause appears.

The plaintiffs are 250 purchasers of timeshare interests in villas at a resort known as Club Regina, or alternatively as the Residence Club at Grand Regina. The resort is in San José del Cabo, a resort area on the Pacific Coast in Baja California (which despite its name is part of Mexico). The plaintiffs bought these interests between 2004 and 2006 from a Mexican company named Desarrollos Turísticos Regina, S. de R.L. de C.V., which the parties call DTR. DTR is not a party to the appeal and indeed no longer exists, having become a Raintree affiliate named CR Resorts Holding, S. de R.L. de C.V., through a series of mergers in 2007 and 2009.

Each contract between a timeshare purchaser and DTR stated that "in case of controversy on the interpretation and compliance with the rights and obligations of this Agreement, the parties hereby agree to submit themselves to the applicable laws and competent courts of the City of Mexico, Federal District, expressly waiving any other forum that may correspond to them by reason of their present or future domiciles." (Not very good English, but DTR is, as we said, a Mexican company.)

Notice that the clause is a choice of law provision as well as a forum selection clause, implying that the law governing the enforceability of the forum selection clause is Mexican law, since the clause is, obviously, a term in the contract. But neither side has asked either the district judge or us to apply Mexican law to the clause; their debate over its enforceability is framed entirely as a dispute about American law, and so the issue of the applicable law has been waived. Abbott Laboratories v. Takeda Pharmaceutical Co. Ltd., 476 F.3d 421, 423 (7th Cir.2007); Phillips v. Audio Active Ltd., 494 F.3d 378, 385-86 (2d Cir.2007).

We are mindful that in Yavuz v. 61 MM, Ltd., 465 F.3d 418, 421, 426-31 (10th Cir.2006), another case in which the district court and the parties had analyzed a forum selection clause under American law even though the contract that contained the clause made foreign law govern, the court of appeals on its own initiative remanded the case with directions that the district court apply the designated foreign law. We're puzzled by that outlier decision. We don't see why the district court should be put to the bother of investigating foreign law when no party is asking it to do so. Parties to a contract are free within broad limits to specify the law that shall govern its interpretation, and also free to modify the specification contained in the contract (in effect amending the contract). By ignoring Mexican law and citing only federal cases in their briefs, the parties have disclaimed reliance on any distinctive features of Mexican law in interpreting their forum selection clause. In effect they've decided that general common law shall govern that interpretation instead. Phillips v. Audio Active Ltd., supra, 494 F.3d at 386, We accept that decision.

The plaintiffs allege that defendant Raintree Vacation Exchange, LLC, in cahoots with defendant Starwood Vacation Ownership, Inc. (together with affiliates of Raintree and Starwood that we can ignore, along with other defendants that we can also ignore), defrauded them by "pretend[ing] to have a Mexican subsidiary (DTR) take in money for [building the villas that the plaintiffs thought they were buying interests in] that would never be built." Raintree and Starwood are in the vacation resort business. Raintree operates a "vacation club" that consists of multiple timeshare resorts, see Bloomberg Businessweek, "Raintree Resorts International, Inc." http://investing.businessweek. com/research/stocks/private/snapshot.asp? privcapId=1879752, while Starwood owns and operates a number of hotels and resorts including the Westin hotel chain. See Starwood Hotels & Resorts, www. starwoodhotels.com/corporate/company_ info.html. The plaintiffs' villas were to be built adjacent to the Westin Resort & Spa Los Cabos. See www.starwoodhotels.com/ westin/property/overview/index.html? propertyID=1087. (The websites we've cited were all visited on Nov. 17, 2012.)

The plaintiffs filed their suit in an Illinois state court. The defendants removed it to the federal district court in Chicago pursuant to the Class Action Fairness Act of 2005, which allows removal to federal district court not only of any class action in which the stakes exceed $5 million and there is diversity of citizenship even if it is not complete, but also of any "mass action," defined as a suit by more than 100 plaintiffs that satisfies the other requirements for removal under the Act. See 28 U.S.C. § 1332(d)(11)(B)(i). Having removed the suit, the defendants moved to dismiss it on the basis of the forum selection clause quoted above. The judge granted the motion after an evidentiary hearing and so dismissed the suit for improper venue, precipitating this appeal.

The plaintiffs' opening appellate brief cites no authority for the proposition, fundamental to the appeal, that Raintree and Starwood cannot be allowed to invoke the forum selection clause because they are not parties to the contract in which it appears. When there are authorities to cite for a key proposition, the party asserting the proposition must cite them (not necessarily all of them, of course), Fed. R.App. P. 28(a)(9)(A), and failure to do so forfeits reliance on the proposition. Windy City Metal Fabricators & Supply, Inc. v. CIT Technology Financing Services, Inc., 536 F.3d 663, 668 n. 3 (7th Cir.2008); Voelker v. Porsche Cars North America, Inc., 353 F.3d 516, 527 (7th Cir. 2003); Heft v. Moore, 351 F.3d 278, 285 (7th Cir.2003); Holland v. Gee, 677 F.3d 1047, 1066 (11th Cir.2012). We could stop there and affirm, but will trudge on.

Rather than Raintree and Starwood being parties to the sale contracts that contain the forum selection clause, DTR was the only party on the selling side (the plaintiffs being the buyers). But (to simplify a tangled corporate structure slightly) a Raintree affiliate owns a Spanish holding company that owns CR Resorts Holding, which as we noted is DTR's successor. Raintree argues that this ownership chain creates a "sufficient relationship" between it and CR Resorts Holding to authorize Raintree to enforce the forum selection clause.

A number of cases say that the test for whether a nonparty to a contract containing such a clause can nonetheless enforce it (and whether the nonparty will be bound by the clause if, instead of suing, it is sued) is whether the nonparty is "closely related" to the suit. Hugel v. Corporation of Lloyd's, 999 F.2d 206, 209-10 (7th Cir. 1993); Holland America Line Inc. v. Wärtsilä North America, Inc., 485 F.3d 450, 455-56 (9th Cir.2007); Marano Enterprises v. Z-Teca Restaurants, L.P., 254 F.3d 753, 757-58 (8th Cir.2001); Manetti-Farrow, Inc. v. Gucci America, Inc., 858 F.2d 509, 514 n. 5 (9th Cir.1988); Caperton v. A.T. Massey Coal Co., 225 W.Va. 128, 690 S.E.2d 322, 347-48 (W.Va.2009); Ex Parte Procom Services, Inc., 884 So.2d 827, 834 (Ala.2003); Weygandt v. Weco LLC, C.A. No. 4056-VCS, 2009 WL 1351808 at *5-6 (Del.Ch. May 14, 2009). This is a vague standard, but it can be decomposed into two reasonably precise principles, which we'll call "affiliation" and "mutuality," the first being applicable to Raintree and the second to Starwood.

A forum selection clause is sometimes enforced by or against a company that is under common ownership (for example as parent and subsidiary) with — that is, an affiliate of — a party to a contract containing the clause, as in American Patriot Ins. Agency, Inc. v. Mutual Risk Management, Ltd., 364 F.3d 884, 888-89 (7th Cir.2004), and the Holland America and Manetti-Farrow cases cited above. Sometimes-not always. Dayhoff, Inc. v. H.J. Heinz Co., 86 F.3d 1287, 1295-97 (3d Cir.1996), refused to enforce a forum selection clause in a suit by one party to the contract against the corporate parents of the other party. It did so on the authority of First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995), which refused to enforce not a forum selection clause, but an arbitration clause, against a company's owners who had not agreed to arbitration, though the company had. The Supreme Court pointed out that "a party who has not agreed to arbitrate will normally have a right to a court's decision about the merits of its dispute (say, as here, its obligation under a contract)," id. at 942, 115 S.Ct. 1920, and it was unlikely that the Kaplans — whom the plaintiff was trying to hold personally liable for their company's debt — meant to give up their right to litigate that highly important personal issue and instead submit themselves to an arbitrator, who would be exercising free-wheeling discretion subject to only very light judicial review.

The stakes are less in the present case, which involves a choice between courts rather than between a court and an arbitrator. Still, there has to be a reason, rather than the mere fact of affiliation, for a nonparty to a contract to be able to invoke, or to be bound by, a clause in it. There is a reason when a subsidiary is a party to a contract that contains a forum selection clause and the other party to the contract sues the parent under the contract. The parent should be allowed to invoke the clause and thus insist that the suit be litigated in the same court in which, pursuant to the clause, its subsidiary is being sued.

So courts have ruled in the parallel situation of an arbitration clause. CD Partners, LLC v. Grizzle, 424 F.3d 795, 798-99 (8th Cir.2005); JLM Industries, Inc. v. Stolt-Nielsen SA, 387 F.3d 163, 177 (2d Cir.2004); E.I. DuPont de Nemours & Co. v. Rhone Poulenc Fiber & Resin Intermediates, S.A.S., 269 F.3d 187, 199-202 (3d Cir.2001); Grigson v. Creative Artists Agency, LLC, 210 F.3d 524, 527-28 (5th Cir.2000); Thomson-CSF, S.A. v. American Arbitration Association, 64 F.3d 773, 779 (2d Cir.1995); JJ Ryan & Sons, Inc. v. Rhone Poulenc Textile, S.A., 863 F.2d 315, 320-21 (4th Cir.1988). Having agreed to arbitrate certain issues, a company shouldn't be allowed, by the facile device of suing an affiliate of the other signatory of the arbitration agreement, to litigate them instead.

A flat rule against enforcing forum selection clauses against affiliates of the parties to contracts containing such clauses would conduce to similar abuses, as we noted in American Patriot Ins. Agency, Inc. v. Mutual Risk Management, Ltd., supra, 364 F.3d at 888, rejecting the argument that "a plaintiff can defeat a forum-selection clause by its choice of provisions to sue on, of legal theories to press, and of defendants to name in the suit."

Suppose A is the parent of B, and B has agreed with C in a contract (to which A is not a party) that any suit between B and C arising out of the contract must be brought in a French court. Such a dispute arises — C accuses B of a breach of contract and has reason to think that A, B's parent, bears some legal responsibility for B's breach; maybe A ordered B to break the contract, without justification, thus committing the tort of intentional interference with contract. C, though committed to litigate in the French court with B, decides to sue A in the United States. If A prefers to litigate in France, it should be allowed to invoke the forum selection clause, though it is not a party to the contract, and thus make C litigate its claim against A in France rather than in the United States so that the two closely related cases are not split between different courts in different countries. C had already committed to having to litigate over the contract in France, so it shouldn't be heard to complain that France is an inconvenient forum when A seeks to defend a suit, based on that same contract, there as well.

But suppose instead that A and B have unrelated disputes with C. A and B are still "closely related" — they are parent and subsidiary — but there is now no reason to allow A to thwart C's choice of forum by invoking a contract to which A is not a party. Nor could A, the parent, be forced to litigate in France just because B, its subsidiary, had agreed to litigate any dispute with C there. A had not signed the contract and thus had not committed itself to litigate in France. C had, and that is why C couldn't complain if A insists that C's suit against A be litigated there.

Courts in the parallel case involving an arbitration clause rather than a forum selection clause sometimes invoke the analogy of piercing the corporate veil. See, e.g., Invista S.Á.R.L. v. Rhodia, S.A., 625 F.3d 75, 85 n. 6 (3d Cir.2010); E.I. DuPont de Nemours & Co. v. Rhone Poulenc Fiber & Resin Intermediates, S.A.S., supra, 269 F.3d at 201-02. If in our first hypothetical case A, the parent, can require C to litigate against it in France on the basis of the forum selection clause in C's contract with B, A is in a sense piercing its own subsidiary's corporate veil by pretending to be a party to the subsidiary's contract. But the analogy is imprecise (as argument by analogy so often is), as well as labored. Piercing the corporate veil means disregarding the limited liability of a corporation's owner or owners (whether corporate or individual), and thus merging the owner's assets — which it had sought to insulate by adopting the corporate form — with those of its subsidiary. Allowing the owner to enforce its subsidiary's forum selection clause merely determines in what court or court system the liability of the owner will be determined. Piercing the veil remains a possible ground for enforcing a forum selection clause against a party's affiliate, cf. Ross v. American Express Co., 547 F.3d 137, 143 n. 3 (2d Cir.2008), if for example the corporation that signed the contract containing the clause was a mere shell; but it is not the only ground.

Were it not for judicial willingness in appropriate circumstances to enforce forum selection clauses against affiliates of signatories, such clauses often could easily be evaded. For example, a signatory of a contract containing such a clause might shift the business to which the contract pertained to a corporate affiliate — perhaps one created for the very purpose of providing a new home for the business — thereby nullifying the clause. Conversely, a signatory who wanted to enforce the clause might be inhibited from shifting his business to a corporate affiliate even though the shift made good business sense.

A literal approach to interpreting forum selection clauses — an approach that always ignored affiliates of the signatories — could also undermine the contribution that such clauses have been praised for making to certainty in commercial transactions, see, e.g., Carnival Cruise Lines, Inc. v. Shute, 499 U.S. 585, 593-94, 111 S.Ct. 1522, 113 L.Ed.2d 622 (1991); The Bremen v. Zapata Off-Shore Co., 407 U.S. 1, 13 and n. 5, 92 S.Ct. 1907, 32 L.Ed.2d 513 (1972), particularly international transactions, as in this case. The literal approach provides certainty as to which parties can invoke the clause (only the signatories), but creates uncertainty as to the forum itself, because a party may be able to avoid the designated forum by manipulating affiliate relationships. On balance it seems better to let the parties decide in the contract whether to limit the forum selection clause to the named entities than for the law to impose such a limit as a default provision to govern in the absence of specification of other entities to be bound. The latter approach would greatly complicate the negotiation of such clauses because the parties would have to strain to close all the loopholes that would open if only entities named in the contract could ever invoke or be made subject to such a clause.

The application of the affiliation doctrine to Raintree is straightforward. Raintree is the parent of DTR's successor, CR Resorts Holding, and can therefore enforce the forum selection clause in DTR's contracts with the plaintiffs since the effect is merely to substitute one party for another (that is, for DTR) bound by the forum selection clause to which the plaintiffs had agreed. Raintree is not trying by substituting itself for DTR to change the forum agreed on in the clause, and so the case is identical to our first A, B, C hypothetical. The plaintiffs by signing the contracts containing the forum selection clause agreed to litigate in Mexico and Raintree is not trying to alter that agreement. Why should it matter that DTR can no longer sue or be sued in its own name, because of its corporate metamorphosis?

The plaintiffs at times claim not to believe that Raintree is the parent (more likely the great-grandparent, given the intermediate subsidiaries) of DTR, and at other times claim that both Raintree and Starwood controlled DTR from the outset, and they complain that the district judge didn't allow them to conduct discovery that would have confirmed their dark though contradictory suspicions. She allowed limited discovery, which neither confirmed any of those suspicions nor provided grounds for still further discovery — especially since the plaintiffs' counsel inexplicably failed to depose the witnesses for Raintree who had given declarations concerning the ownership chain linking Raintree to DTR. Anyway how can the plaintiffs complain about the substitution of Raintree for a party they agreed to litigate with (if there were a dispute) in Mexico, when that party can no longer be sued because it has been merged into Raintree?

So much for Raintree; what of Starwood? It is not in the ownership chain that includes CR Resorts Holding, though it bought a significant part of the assets of the resort property that DTR had planned to develop. But it can invoke the forum selection clause on a different ground from that of affiliation: mutuality. The gist of the plaintiffs' complaint is that Raintree owed Starwood $10 million and that the two firms caused DTR to use the money it raised from the sales of the timeshares to pay off Raintree's debt instead of building the villas. The plaintiffs are thus alleging a conspiracy between Raintree and Starwood to defraud them, and the question is whether an alleged conspirator can invoke the forum selection clause contained in a contract, signed by his alleged co-conspirator, that created or advanced the conspiracy. The answer is yes — maybe not in every case, but in this one, where the suit accuses Raintree and Starwood of being secret principals of DTR, their agent in dealing with the timeshare buyers and thus in executing the fraud.

A contract that the agent of secret principals makes with a third party can be enforced, at the third party's option of course (the third party can rescind — get out of the contract — if he prefers), against the secret principals. Restatement (Third) of Agency §§ 6.03 and comment. b, 6.11(4) (2006); Clarendon National Ins. Co. v. Medina, 645 F.3d 928, 935 (7th Cir.2011); Frietsch v. Refco, Inc., 56 F.3d 825, 828 (7th Cir.1995); SFH, Inc. v. Millard Refrigerated Services, Inc., 339 F.3d 738, 745 (8th Cir.2003). So the plaintiffs, because they alleged that Starwood (together with Raintree, by virtue of the conspiracy) controlled DTR, could have held Starwood to the forum selection clause had they wanted to sue in Mexico — and from this it follows that Starwood can hold the plaintiffs to the clause in the opposite situation and thus defend the suit in Mexico. Were it not for this principle of mutuality, the plaintiffs would have a choice of forums, and Starwood would not; and that could not have been the intention behind a clause that makes Mexico the exclusive forum irrespective of the parties' domiciles. "All [Starwood] is doing in invoking the forum selection clause to which it is not a party is accepting one of the premises of the plaintiff's suit — that [DTR is] indeed simply [a] cat's paw of [Starwood] — and pointing out that the implication is that the [timeshare] contracts, including the forum selection clause, are really between the plaintiffs and [Starwood]." Frietsch v. Refco, Inc., supra, 56 F.3d at 828. Because Raintree is alleged to be a secret principal along with Starwood, it can enforce the forum selection clause on the same ground as Starwood, as well as on the affiliation ground that we discussed earlier.

From a practical standpoint it is evident that the case should be litigated as one case in one court in one country, and not as two cases in two courts in two countries. Suppose the plaintiffs wanted to sue both Raintree and Starwood in Mexico. We said they would be entitled to sue Raintree there regardless of mutuality — could Starwood insist that it be sued in the United States? That wouldn't make sense. And notice that because Raintree was entitled to remove the case to Mexico under the forum selection clause irrespective of Starwood's rights, the doctrine of forum non conveniens clicks in and would require the dismissal of the claim against Starwood as well, even if it weren't entitled to enforce the forum selection clause. The suit would then be refiled in the Mexico court in which the plaintiffs would refile their claim against Raintree. For with half the case to be tried in a Mexican court, it would be very non conveniens to try the other half in Chicago. See U.S.O. Corp. v. Mizuho Holding Co., 547 F.3d 749, 750 (7th Cir. 2008); Aguas Lenders Recovery Group, LLC v. Suez, S.A., 585 F.3d 696, 700 (2d Cir.2009).

The plaintiffs have another string to their bow, however, though one that makes only a faintly audible twang: they argue that a forum selection clause does not apply to a fraud suit. Wrong. Obviously if the clause were itself a product of fraud it would be unenforceable. Scherk v. Alberto-Culver Co., 417 U.S. 506, 519 n. 14, 94 S.Ct. 2449, 41 L.Ed.2d 270 (1974). But even if the contracts of sale to the plaintiffs that contain the clause are fraudulent, it doesn't follow that the clause is. Huffington v. T.C. Group, LLC, 637 F.3d 18, 23-24 (1st Cir.2011). The clause is not unclear, in illegible print, in Sanskrit or hieroglyphics, or otherwise suggestive of fraudulent intent. Paper Express, Ltd. v. Pfankuch Maschinen GmbH, 972 F.2d 753, 757 (7th Cir.1992); Northwestern National Ins. Co. v. Donovan, 916 F.2d 372, 377 (7th Cir.1990). And there is no evidence that the defendants tried to mislead the plaintiffs concerning the meaning of the clause, or selected a foreign forum to make it difficult for the plaintiffs to enforce their rights under the contracts — Mexico after all was where the contracts were to be performed. See Carnival Cruise Lines, Inc. v. Shute, supra, 499 U.S. at 595, 111 S.Ct. 1522; Liles v. Ginn-La West End, Ltd., 631 F.3d 1242, 1254-55 (11th Cir.2011) (per curiam); Effron v. Sun Line Cruises, Inc., 67 F.3d 7, 9-10 (2d Cir.1995). And as the clause applies to any "controversy on the interpretation and compliance with the rights and obligations of" the contracts of sale, it is broad enough to encompass tort suits that arise out of the contract. E.g., Scherk v. Alberto-Culver Co., supra, 417 U.S. at 519 n. 14, 94 S.Ct. 2449; American Patriot Ins. Agency, Inc. v. Mutual Risk Management, Ltd., supra, 364 F.3d at 889; Omron Healthcare, Inc. v. Maclaren Exports, Ltd., 28 F.3d 600, 602 (7th Cir.1994); Terra Int'l, Inc. v. Mississippi Chemical Corp., 119 F.3d 688, 695 (8th Cir.1997); Lambert v. Kysar, 983 F.2d 1110, 1121-22 (1st Cir. 1993).

The dismissal of the suit is

AFFIRMED.