This paper examines the idea of 'core business' in contemporary South African public universities. South Africa's public higher education system has global ambitions, but is also highly internally stratified. Drawing on new data from interviews with higher education leaders and government policymakers across a number of South African institutions, we show that while the rhetoric of 'core business' of the university has been adopted by higher education leaders, the question of what constitutes the purpose of the university, in South Africa and arguably beyond, is subject to ongoing debate and negotiation. The multiplicity of conflicting but coexisting narratives about what universities should do in South African society--producing excellent research, preparing a labour force, or addressing societal inequalities--exposes a persisting tension surrounding the purpose of a public university. And while this tension has historical origins, we show that responses to addressing these various roles of the institution are not developed organically and in a neutral context. They emerge under conflicts over limited state funding and attendant and opportune market pressure put on public universities in times of crisis, that shape profoundly their framing and outcomes, and the future of the universities.