This paper examines a programme initiated and managed by an entrepreneurial university in the United Kingdom (UK), aiming to foster the circular water economy in Sub-Saharan Africa. Our focus is on transitioning from conventional models of the entrepreneurial university to innovative forms of knowledge exchange that prioritise social innovation and sustainable development, as per the “engaged university”. Through an in-depth qualitative study, we find that three interrelated levels of engagement—engaging individuals, engaging organisations and engaging communities—are essential for universities delivering the third mission of societal impact. Employing the established framework developed by Hughes et al. (in: Knowledge exchange between the arts and humanities and the private, public and third sectors, Arts & Humanities Research Council, Cambridge, 2011) to examine university activities, we expose the social innovation underpinning people-based, problem-solving and community-based activities. In the context of the third mission, social innovation involves bringing individuals, organisations and communities together through supporting entrepreneurship, collaboration and mutual learning capacities both within and beyond the university setting. The mechanisms driving university engagement are thus a process of multilevel social innovation, relying on support from individual researchers, project leaders, partner institutions and local end-user communities. Adopting a multilevel perspective allows us to identify the distinct mechanisms of engaged universities, which transcend those of other university models in the realm of social innovation. We argue that the engaged university model extends understanding of how supports for social innovation can connect and create networks to tackle global challenges.