I really think that giving a univerisy tag to any series will be extremely difficult, unless the series specifically says college/uni somewhere. As I said before, most school/uni anime & manga is nearly impossible to tell whether it's "high school", boarding school, or uni.
That being said however, perhaps "univeristy" could be used as one of those
sub-tags that soth said v3 will have. Something like:
SCHOOL LIFE:
-UNIVERSITY
Another idea: Replace "university" with "boarding school", or something similar. (It's almost always very clear when a series involves some form of boarding/away school (including uni), but is almost never clear whether it's some sort of regular level boarding school, or a uni level school.)
Alternatively, have both as sub-tags:
SCHOOL LIFE:
-ELEMENTARY
-BOARDING SCHOOL
-UNIVERSITY