A revival of cosmopolitanism seems to be underway in both discourse and practice. However, much of this revival draws from only one trajectory of cosmopolitanism, and fails to build upon different traditions of cosmopolitan thinking and experimentation. Cosmopolitanization is an ongoing process of critique, creativity and border-crossing which involves transformations in self, culture, society, economy and polity. It requires multi-dimensional processes of self-development, inclusion of the other, and planetary realizations. Against this background, this contribution explores the multiverse of transformations that confront contemporary discourses of cosmopolitanism. It also discusses the issue of cosmopolitan responsibility, noting three major challenges: global justice; cross-species dignity; and dialogue among civilizations, cultures, religions and traditions.