The institutional development and performance of the Group of 20 (G20), the BRICS group of Brazil, Russia, India, China and South Africa, and the Shanghai Cooperation Organisation (SCO) have shaped twenty-first-century global governance. Each of these plurilateral summit institutions (PSIs) has different founding visions, missions, memberships, participants, institutionalisation patterns and priorities. However, the potential for competition soon gave way to contagious, convergent, cumulative cooperation. By 2021, each was countering COVID-19-created crises in a mutually reinforcing way. Each extended outreach to new members or regular guest leaders, expanded their institutions and civil society engagement, and embraced economic finance, social sustainability and political-security issues. They increased their performance on the major dimensions of global governance in mutually supportive, if highly implicit, ways. The three big non-western Asian powers-China, Russia and India-at the core of these PSIs drove this dynamic, contagious, cumulative convergence and applied lessons learnt across all three PSIs. This was reinforced by their increasing, shared need to guide globalisation and counter its shocks, from the Asian financial crisis in 1997-1999 to the COVID-19 pandemic of 2020-2021.