If it was a rotational thing, you'd probably need four different conferences represented. Marquette, Illinois/Northwestern, Notre Dame, Iowa State? Just thinking of the nearest high-majors to Chicago that all have well-represented fanbases living in the city.
I'd love the idea of a Majerus classic. Rotate sites every year, have Marquette, Utah, Ball State, and St. Louis involved. Though when you get the marquee MU/Utah matchup, that other one might look like a bit of a stinker.