...or just change the nameplate on the school, and leave the coach and the players where they are? So if SMU moves from the AAC to the New Big SW, and Bob Jones Univ moves into the AAC, former SMU coach larrybrown75 and all of his recruited players, prestige, etc. stay in the AAC at Bob Jones U.
He's Larry Brown, he'll change schools at the drop of a hat anyway...