My other team is Michigan (BYU undergrad, UofM grad school).
When BYU and Michigan played recently, I rooted for BYU. (That didn't go well! Maybe that is the problem. I need to do a reverse psychology thing on that day!!)
However, I COULD imagine a scenario ... but it would be a pretty extreme scenario. If the game was late in the year, and Michigan was 11-0 and looking at shot at the CFP AND BYU was struggling and 2-9 and not going to a bowl game ... THEN I could see myself cheering for Michigan because it would mean more opportunities for at least on of my teams. BUT I think that scenario is nearly impossible (but after a COVID scrambled season last year, never say never).... I don't see a scenario is which BYU and Michigan would play late in the season, and early in the season, I would certainly be rooting for a BYU win, as one example of why I can't see that ever happening.