Students as Partners (SAP) initiatives are often framed as opportunities to reanimate university education so that students become active participants in their learning, and change agents capable of transforming their institutions. Embedded in these framings is a view that students are also the primary 'experts' of their learning experiences. This shift marks curious terrain about how staff come into partnership when students are encouraged to understand themselves as experts at the very same time the purpose of universities is beset with multiple and contradictory narratives, and the whole notion of expertise -- even for academics -- has become unsettled by the politics of a post-truth era. If the advocacy of student expertise is to be understood as a radical intervention to the marketised neoliberal university, as is often claimed, we argue that the desire for expertise has a more compelling basis when students are engaged with what Gina Hunter calls learning to 'see institutionally'. In this article, we both describe, and put to work, Jeffrey J. Williams's idea 'teach the university' as one mechanism for students and staff working in partnership to 'see institutionally'. We then examine the nascent efforts of our own SAP initiatives to make a case for why 'the university' -- as idea and institution -- deserves to be introduced to, studied and critically interrogated by students as part of a long tradition of inquiry. While a good many SAP initiatives aim to address where students are absent, under-represented or disempowered in the university, very few appear to take seriously that there is a field of scholarship about universities that lends credibility "and" contest to the notion of expertise. By staging a conceptual encounter between Williams, Hunter and our own partnership work, the potential for SAP is expanded as project that cares for the future university.