A future multilateral investment court (MIC) or multilateral appellate mechanism (MAM) will operate on a plurilateral basis, among States that become parties to the tribunal's constitutive instrument and grant it jurisdiction over disputes under their investment treaties. The creation of a MIC or MAM would involve a significant strengthening and centralization of dispute settlement institutions in the investment treaty regime, which is already overly dependent on law-development by adjudicators, reflected in well-established concerns about loss of State control. Thus, a key challenge in designing a MIC or MAM is to incorporate appropriate control mechanisms that will enable State input, without unduly undermining a MIC or MAM's independence. This article analyses control mechanisms in a MIC or MAM, considering a wide range of questions of institutional design. It highlights two fundamental tensions. One is the tension between independence and accountability. The other tension is between procedural multilateralism and substantive bilateralism. While the procedural law in a MIC or MAM will have been multilateralized, the substantive law the tribunal will interpret and apply will remain contained in mostly bilateral investment treaties, controlled by the parties to those agreements. This article addresses the challenges of designing a multilateral tribunal for a regime that lacks multilateral substantive law and contributes to wider debates over striking an appropriate balance between international judicial independence and Member State control.