EASTERBROOK, Circuit Judge.

Employers that withdraw, in whole or part, from underfunded multiemployer pension plans must pay their share of the shortfall. They can dispute the plans' assessments by seeking recalculation within 90 days, 29 U.S.C. § 1399(b)(2)(A), and they have a further 60 days to invoke a process that the statute calls arbitration, though unlike normal arbitration it is neither contractual nor consensual. 29 U.S.C. § 1401(a). (A joint request for arbitration maybe made within 180 days, and there are other details that we need not relate.) The Central States Pension Fund concluded that U.S. Foods has withdrawn in part; it assessed some liability in 2008 and some in 2009. US Foods made a timely request for arbitration of the 2009 assessment. That process is under way. But it did not ask for arbitration of the 2008 assessment within the statutory limit.

In response to the Fund's suit seeking to collect the 2008 assessment and prevent the arbitrator from considering how much U.S. Foods owes for that year, U.S. Foods asked the district court to order the arbitrator to calculate the amount due for 2008 and 2009 jointly. The court ruled that U.S. Foods had missed the deadline for arbitral resolution of the 2008 assessment. US Foods appealed, relying on 9 U.S.C. § 16(a)(1)(B), which authorizes an interlocutory appeal from an order "denying a petition under section 4 of this title to order arbitration to proceed". This poses the question how a request for "arbitration" under a section in Title 29 of the United States Code could come within § 16(a)(1)(B), which is part of Title 9, the Federal Arbitration Act (FAA or Arbitration Act) and is limited to requests to arbitrate under § 4 of that title (9 U.S.C. § 4).

Section 4 says 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." US Foods and the Fund do not have a "written agreement for arbitration", and it would be impossible for a court to order "that such arbitration proceed in the manner provided for in such agreement." US Foods insists that this is irrelevant because the Multiemployer Pension Plan Amendments Act of 1980 (MPPAA or Multiemployer Act) provides that the procedure it establishes "shall, to the extent consistent with this subchapter, be conducted in the same manner, subject to the same limitations, carried out with the same powers (including subpoena power), and enforced in United States courts as an arbitration proceeding carried out under title 9." 29 U.S.C. § 1401(b)(3). This reference to the "manner" and "powers" of arbitration under the Arbitration Act does not supply what § 4 demands: a "written agreement".

One could argue to the contrary that, unless the court overlooks the difference between statutory arbitration (the Multiemployer Act) and contractual arbitration (the Arbitration Act), there would be no authority to mandate arbitration at all — for although § 4 supplies a judicial power to compel arbitration, the Multiemployer Act lacks a parallel provision. Perhaps § 1401(b)(3) is best understood as requiring litigants and the judiciary to proceed as if the extra-judicial proceedings contemplated by the Multiemployer Act are contractual for the purpose of the Arbitration Act. Then § 16(a)(1)(B) would authorize an interlocutory appeal. As far as we can tell, no court of appeals has addressed this possibility or otherwise decided whether § 16 of the Arbitration Act authorizes an interlocutory appeal in a proceeding under the Multiemployer Act. We need not be the first, for there is another problem with appellate jurisdiction.

Arbitration of the 2009 assessment is under way. US Foods did not ask the district court to compel the Fund to engage in a second, independent arbitration. Instead, it maintains that the 2008 and 2009 assessments are inversely related, so that to change one compels a change to the other. US Foods therefore wants the 2008 assessment added to the agenda of the arbitrator who is already serving. Yet the arbitrator can decide for himself, in the first instance, what disputes require resolution. Whether or not the arbitrator considers the interaction of the 2008 and 2009 figures, his decision could be reviewed (to the extent the Multiemployer Act allows) on petition to enforce or set aside the final order.

A judge who adds or subtracts issues in a pending arbitration has neither compelled nor forbidden arbitration; the judge has instead resolved an issue in the arbitration. That's why we held in Blue Cross Blue Shield of Massachusetts, Inc. v. BCS Insurance Co., 671 F.3d 635 (7th Cir.2011), that a proposal to tell an arbitrator what to do is not a request for "an order directing... arbitration" within the meaning of § 4 of the Arbitration Act, and a judge's order declining to interfere in the conduct of an arbitration is not an order "denying a petition under section 4 of this title to order arbitration to proceed" for the purpose of § 16(a)(1)(B).

We explained in Blue Cross that a party's request to tell an arbitrator how to act in a pending proceeding is not a request to compel arbitration, no matter what caption the litigant puts on its motion. And we added that "judges must not intervene in pending arbitration to direct arbitrators to resolve an issue one way rather than another. Trustmark Insurance Co. v. John Hancock Life Insurance Co., 631 F.3d 869 (7th Cir.2011). Review comes at the beginning or the end, but not in the middle." 671 F.3d at 638. Once the arbitration is over, the losing side can seek judicial review. 29 U.S.C. §§ 1401(b)(2), 1451. Until then matters are in the hands of the arbitrator.

The appeal is dismissed for want of jurisdiction.