In 2009 Blanchard & Associates, a Chicago law firm, provided legal services to an Indian pharmaceutical company, Lupin Ltd. ("Lupin India"), and its American subsidiary, Lupin Pharmaceuticals, Inc. ("Lupin USA"). The advice concerned the patentability of a generic birth-control drug that Lupin India planned to launch in the United States through Lupin USA. When the Lupin companies initially sought Blanchard's advice, the firm sent an engagement letter outlining its hourly fees and other terms. Neither Lupin India nor Lupin USA signed the letter, but Blanchard provided the requested legal services and the companies paid the firm for its work-at least at first. In October 2009 Blanchard sent its two final invoices but they went unpaid. Seven years later Blanchard sued the Lupin companies for breach of contract and unjust enrichment. A district judge dismissed both claims as untimely.

We agree that the unjust-enrichment claim is untimely. It accrued in 2009 when *920Blanchard furnished the services and the Lupin companies did not pay, so the five-year statute of limitations expired long before suit was commenced. But the contract claim is timely. Though the engagement letter is unsigned, it counts as a written contract under Illinois limitations law, and the claim for breach is therefore governed by a ten-year statute of limitations. See 735 ILL. COMP. STAT. 5/13-206. Blanchard filed suit within that time, so we reverse and remand for further proceedings on the contract claim.

I. Background

We take the following account of the facts from the amended complaint. Blanchard is a law firm formerly based in Chicago, though its sole proprietor is a citizen of Tennessee. Lupin India is a pharmaceutical company incorporated under the laws of India. Its subsidiary, Lupin USA, is incorporated in Delaware with its principal place of business in Baltimore, Maryland. The two Lupin companies formed a joint venture to launch a generic birth-control drug in the United States. In March 2009 they turned to Blanchard for legal advice in connection with that venture-more specifically, patent reviews and related services.

Blanchard communicated with the companies through Sofia Mumtaz, who held herself out as an authorized agent for both Lupin India and Lupin USA. Blanchard sent Mumtaz an engagement letter explaining the hourly rates for the firm's attorneys and other terms of the representation. The letter also specified that payment was due on the firm's invoices within 30 days.

Mumtaz never signed the engagement letter. Nevertheless, Blanchard provided the requested services between April and August 2009. The Lupin companies accepted those services and paid the firm's first two invoices. At that point, payment stopped. On October 31, 2009, Blanchard submitted two final invoices totaling $120,835, but they went unpaid.

On August 4, 2016, Blanchard sued Lupin USA in Illinois state court alleging claims for breach of contract and unjust enrichment. After removing the case to federal court, see 28 U.S.C. § 1332, Lupin USA moved to dismiss the complaint under Rule 12(b)(6) of the Federal Rules of Civil Procedure, arguing that (1) it failed to allege a valid and enforceable contract; (2) the claims were untimely; and (3) Blanchard sued the wrong party because Lupin India was responsible for any nonpayment.

Blanchard amended the complaint to add Lupin India as a defendant. The new complaint also clarified that Lupin India and its American subsidiary had acted as a joint enterprise and that Mumtaz held herself out as a dual agent for both companies. Blanchard served Lupin USA as a named defendant and as the agent for Lupin India.

Lupin USA again moved to dismiss, raising the same grounds. Lupin India neither answered nor joined the motion to dismiss, so Blanchard sought entry of default against it under Rule 55(a) of the Federal Rules of Civil Procedure.

The judge dismissed the suit against both defendants. She first ruled that Lupin USA is a proper defendant because the amended complaint adequately alleged that the two companies operated as a joint venture and together had engaged Blanchard's legal services. Turning to the contract claim, the judge held that the amended complaint sufficiently alleged the existence of a valid and enforceable contract. But she also ruled that the claim should be construed as one for breach of an unwritten contract because the engagement letter was never signed. Under Illinois law a five-year limitations period applies *921to unwritten contracts, so the judge dismissed that claim as untimely. As for the unjust-enrichment claim, the judge held that it too was time-barred because it accrued in November 2009 and was governed by a five-year statute of limitations. Finally, the judge held that her rulings regarding the time bars "apply equally" to the claims against both defendants, so she denied Blanchard's request for entry of default against Lupin India.

II. Discussion

We review a Rule 12(b)(6) dismissal de novo. Deppe v. Nat'l Collegiate Athletic Ass'n , 893 F.3d 498, 500 (7th Cir. 2018). Before we take up the timeliness questions, we need to sort out which Lupin entity is a proper defendant. Lupin USA continues to insist that it is not a proper party because the engagement letter referred only to "Lupin" and was directed to an address in India. Read in context, however, the letter's reference to "Lupin" signifies the joint enterprise between both companies. The amended complaint alleges that the two companies formed a joint venture to launch their generic drug in the United States and that Mumtaz held herself out as an agent for both companies when she negotiated with Blanchard. Those facts, if true, establish that both Lupin USA and Lupin India were parties to the agreement.

Lupin USA objects that the amended complaint doesn't explain when, where, or how Mumtaz held herself out as an agent and that the documents attached to the complaint do not plausibly show a joint enterprise. Based on these supposed factual shortcomings, Lupin USA argues that Blanchard failed to "nudge" its claims "across the line from conceivable to plausible." Ashcroft v. Iqbal , 556 U.S. 662, 680, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009) (quoting Bell Atl. Corp. v. Twombly , 550 U.S. 544, 570, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007) ).

This argument misunderstands the Twombly / Iqbal plausibility standard. The amended complaint describes the joint venture between Lupin India and Lupin USA, Mumtaz's role as the agent for both companies, the purpose of the legal engagement that commenced in March 2009, Blanchard's subsequent provision of legal services between April and August of that year, and the nonpayment of its two final invoices totaling $120,835. These allegations are facially plausible and thus are "entitled to the assumption of truth" at this stage. Id. And the documents attached to the complaint corroborate the allegations. The attachments include the engagement letter and invoices, which were sent to an address in India, and also a 2011 press release announcing the joint venture's launch of Lupin's drug in the United States. Reading the complaint and its attachments as a whole, it's reasonable to infer that Lupin India and its American subsidiary worked together to bring the drug to market in the United States and together sought Blanchard's legal advice in connection with that effort. Nothing more is needed. Both companies are proper defendants.

With that point out of the way, we proceed now to the timeliness questions. Claims for breach of contract and unjust enrichment are mutually exclusive: "[U]njust enrichment is based on an implied contract," so it does not apply when an actual contract governs the parties' relationship. People ex rel. Hartigan v. E&E Hauling, Inc. , 153 Ill.2d 473, 180 Ill.Dec. 271, 607 N.E.2d 165, 177 (1992) (quotation marks omitted). But the inconsistency doesn't matter at the pleading stage; a complaint may plead these two state-law theories in the alternative. See Gagnon v. Schickel , 368 Ill.Dec. 240, 983 N.E.2d 1044, 1052 (Ill. App. Ct. 2012).

*922That said, the unjust-enrichment claim is clearly time-barred. Under Illinois law a claim for unjust enrichment must be brought within five years of accrual. 735 ILL. COMP. STAT. 5/13-205 ; Mann v. Thomas Place, L.P. , 364 Ill.Dec. 276, 976 N.E.2d 554, 557 (Ill. App. Ct. 2012). The claim is woefully late whether it accrued when the Lupin companies retained the benefit of Blanchard's legal services without paying for them (as Blanchard argues) or when payment came due on the invoices but was not made (as Lupin USA argues).

It's certainly true, as Blanchard points out, that a claim for unjust enrichment requires the plaintiff to show that "the defendant retained a benefit to the plaintiff's detriment." HPI Health Care Servs., Inc. v. Mt. Vernon Hosp., Inc. , 131 Ill.2d 145, 137 Ill.Dec. 19, 545 N.E.2d 672, 679 (1989). It follows, Blanchard argues, that a claim for unjust enrichment does not accrue until there is both a detriment to the plaintiff and a benefit to the defendant. Lupin USA contends, on the other hand, that the accrual date should be keyed to the date payment was required and not made-here, November 30, 2009-just like an ordinary contract claim.

We don't see how this debate matters; the claim is late either way. Under Blanchard's proposed rule, the claim accrued no later than the end of 2009. By then the joint venture had received the last of the firm's legal services-the work concluded in August-and no payment was forthcoming. At that point the elements of benefit and detriment were present. On this understanding of accrual, the five-year statute of limitations expired at the end of 2014, two years before Blanchard filed suit.

Blanchard's arguments to the contrary are unavailing. The firm maintains that the joint venture did not benefit from its legal advice until 2011 when the drug received FDA approval and launched in the United States. Not so. Legal advice immediately benefits the client. Relatedly, the firm argues that the attorney-client relationship didn't actually end until the FDA approved the drug-indeed, "if it is not on-going even now." That position cannot be reconciled with the amended complaint; it alleges that the firm provided legal services between April and August 2009, a closed time period.

To support its argument for a later claim-accrual rule, Blanchard cites Rubin & Norris, LLC v. Panzarella , 402 Ill.Dec. 127, 51 N.E.3d 879, 893 (Ill. App. Ct. 2016), but that case doesn't help its cause. Rubin simply reaffirms the established principle that a claim for quantum meruit-similar but not identical to an unjust-enrichment claim, see HPI Health Care Servs. , 137 Ill.Dec. 19, 545 N.E.2d at 679 -accrues on "the date the services have been completed." Rubin , 402 Ill.Dec. 127, 51 N.E.3d at 893. Rubin also explains that in order to recover legal fees from a client in an action for quantum meruit, an attorney must first establish that there was an underlying attorney-client relationship and the client agreed to pay. Id. , 402 Ill.Dec. 127, 51 N.E.3d at 891 (citing In re Chi. Flood Litig. , 289 Ill.App.3d 937, 224 Ill.Dec. 860, 682 N.E.2d 421, 427 (Ill. App. Ct. 1997) ). In other words, an attorney-client relationship doesn't dictate when a claim accrues; rather, it is a necessary condition for a claim to exist at all . We don't see Rubin 's relevance to this case.

Moving to the contract claim, here we cannot agree with the judge's analysis. She applied Illinois's five-year limitations period for unwritten agreements because the engagement letter was unsigned. That was a mistake. Though unsigned, the engagement letter qualifies as a written contract under Illinois's limitations law.

Illinois provides a five-year limitations period for actions based on unwritten *923contracts, 735 ILL. COMP. STAT. 5/13-205, but a ten-year limitations period applies to an action based on a written contract, id. § 5/13-206. A contract is deemed written for these purposes "if parties are identified and all the essential terms are in writing and ascertainable from the instrument itself." See Portfolio Acquisitions, LLC v. Feltman , 391 Ill.App.3d 642, 330 Ill.Dec. 854, 909 N.E.2d 876, 880 (2009). The essential terms include "the nature of the transaction, the amount in question and, at least by reasonable implication, an intention to repay the debt." Garrett's Estate v. Garrett , 24 Ill.App.3d 895, 322 N.E.2d 213, 215 (1975). If extrinsic evidence "is necessary to identify the parties or essential terms, the contract is considered an oral contract for purposes of the statute of limitations." Portfolio Acquisitions , 330 Ill.Dec. 854, 909 N.E.2d at 880.

Lupin USA does not dispute that the engagement letter identifies the nature of the transaction. It argues instead that the letter does not qualify as a written contract for limitations purposes because it fails to identify the parties or the amount in question. And because the letter is unsigned, Lupin USA insists that it does not evince an intent to pay.

We disagree on all counts. The letter identifies both Blanchard & Associates and Lupin as parties to the contract. As we've explained, "Lupin" as used here refers to the joint venture between Lupin India and Lupin USA. That's sufficient to identify the parties without resorting to extrinsic evidence. The letter also lists the hourly rates of the firm's attorneys, which establishes the amount in question to the degree necessary for a suit on a written contract. Finally, the Illinois Supreme Court has held that a contract counts as "written" for purposes of the statute of limitations even if the parties haven't signed it. Ames v. Moir , 130 Ill. 582, 22 N.E. 535, 536 (1889) (citing Plumb v. Campbell , 129 Ill. 101, 18 N.E. 790 (1888) ) (holding that an unsigned contract constituted a written agreement for limitations purposes because it contained all of the essential elements). That forecloses Lupin USA's argument that the engagement letter doesn't evince an intent to pay. The ten-year limitations period applies, and the contract claim was timely filed.

Accordingly, we AFFIRM the dismissal of the unjust-enrichment claim, REVERSE the dismissal of the contract claim, and REMAND for further proceedings. On remand Blanchard may renew its request for entry of default against Lupin India.