In this article, we argue that there is an urgent need to align internationalisation and university social responsibility agendas through the construct of Internationalisation of Higher Education for Society. The service or "third mission" of higher education institutions - to contribute to the social, economic, and cultural development of communities - has long been a core function of universities alongside teaching and research. However, the service mission is often disconnected from the internationalisation agenda. Service to society is rarely the focus of internationalisation strategies, and third mission strategies are predominantly domestically oriented. We consider how universities might, in today's fractured and fragile world, amplify their contributions to society and the global common good by strategically enacting their global social responsibility through internationalisation. Related concepts of relevance are discussed, and we conclude with recommendations for leaders, researchers, and those involved in teaching and learning who seek to contribute to these endeavours.