Drawing on what is essentially the Jensen and Meckling theory of principals and agents, Henry Hansmann has put together what he views as a general theory of the cooperative form of organization. In this account, even the modern corporation is a special case of the cooperative (Why?) A non-profit is also a type of cooperative.
Your assignment is to analyze one particular non-profit: the research university. To make things easier, you can think in terms of private research universities (like Yale). You should be able to go beyond Hansmann's own terse discussion of colleges.
Reading from the section of the syllabus titled "property rights and ownership" will be helpful.