Unfortunately, his hands are tied by the BOT, who happen to love Bronco, so there's very little he can do about it. The only way, he can fire Bronco is if he has a couple of losing seasons or a Crowtonesque meltdown. Also, if attendance takes a dramatic nosedive, that could force his, (and the BOT's) hand.
As long as Bronco has winning seasons and goes to bowl games, he can stay at BYU as long as wants, despite Holmoe's personal misgivings about the situation.