The aim of this paper is to explore the implications of the concept of a "fully-functioning university" for its contribution to the advancement of knowledge. The paper therefore starts by reviewing that concept and the tripartite mission on which it is based. The main question that the paper seeks to answer is, "what kinds of research can best support the advancement of knowledge, the higher education of students and those beyond the walls of the university, respectively?" The paper also explores how universities can serve the advancement of knowledge, beyond "research"--i.e. in addition to research as that term is currently understood within universities. It concludes with some ideas for how a fully-functioning university can contribute to the advancement of knowledge in ways that also contribute to the advancement of students and the community and society more widely.