I'm toying with the idea that there might be an analogy between the "partial" communion with the Catholic Church that Lumen Gentium talks about in #8, and a university that is "partially" Catholic. It contains some of the elements that are distinctively Catholic (as opposed to, for instance, a secular university, which may have some natural goods that belong to the Catholic university, but none of the distinctive elements that flow directly or indirectly from Revelation). Since the university is characterized by the pursuit of truth, the designation of a partially Catholic university would modify the LG text to read, "although many elements of...of truth are found outside of [the fully Catholic university's] visible structure. These elements, as gifts belonging to the [fully Catholic University], are forces impelling toward catholic unity."
So, you might have the equivalent of Fully Catholic Universities (TM), Mostly Catholic Universities (TM), Somewhat Catholic Universities (TM), and Barely Catholic Universities (TM).
I think the Cardinal Newman Society's criteria for a fully Catholic university are probably pretty close to the ones I would consider essential for being a FCU. That, plus agreeing with my theology. :)