The historical trajectories of three crises have converged in the 2020s: the COVID-19 pandemic, rising inequality and the climate crisis. Global health as an organising logic is being transformed by the COVID-19 pandemic. We point to an emerging consensus that the triple threats of global heating, zoonoses and worsening, often racialised inequalities, will need to be met by models of cooperation, equitable partnership and accountability that do not sustain exploitative logic of economic growth. Health governance is challenged to reconsider sustainability and justice in terms of how local and global, domestic and transnational, chronic and infectious, human and non-human are interdependent. In this article, we discuss their intersection and suggest that a new set of organising ideals, institutions and norms will need to emerge from their conjunction if a just and liveable world is to remain a possibility for humans and their cohabitants. Future health governance will need to integrate pandemic preparedness, racial justice, inequality and more-than-human life in a new architecture of global health. Such an agenda might be premised on solidarities that reach across national, class, spatial and species divisions, acknowledge historical debts and affirm mutual interdependencies.