This article argues that one of the key questions—or even the key question—of our times is how to foster enhanced compatibility between national policy-making sovereignty and effective multilateral cooperation. There are multiple reasons for this. First, given the growing importance of global public good-type policy challenges and the rising trend toward multipolarity, the relationships among countries are now de facto marked by universal multilateralism. International cooperation is no longer only an option, as it conventionally was (especially for the major powers), but a compulsion. This new, binding type of multilateralism is called here “multilateralism 2.0” to distinguish it from the conventional, more optional type of multilateralism. Second, necessary systematic reforms to make global governance fit for the new reality of multilateralism 2.0 are still lacking, because states value their sovereignty. However, a persuasive reform vision and reform leadership have not yet emerged; currently, uncertainty exists about how to have both sovereignty and effective cooperation. The world is experiencing a “Kindleberger moment”: crisis and no leadership. Accordingly, this article offers concrete suggestions on possible ways forward. It suggests that the most important and urgent reform is to forge consensus on a new principle: the “dual-compatibility principle” calling for a commitment of states to (i) more sovereignty-compatible multilateral cooperation and (ii) an exercise of national policy-making sovereignty that is more compatible with multilateral cooperation. To clearly see the critical importance of this principle, a prior, eminently doable reform step is needed: widening the analytical lens of multilateralism to capture both the “real” and the “political” sides of this phenomenon and to recognize that the former is, in effect, the independent variable and the latter the dependent one.