It could happen. If so, Big12 into Florida with USF and UCF taking on ESPN's Florida and Florida State; ESPN would ask the SEC to raid the Big12; Fox would ask the Pac/B1G to fight the SEC for the top Big12 teams; and B1G might raid AAC for UConn, taking it away from ESPN.
So far at least, both the networks and the conferences have avoided such head-on turf wars, which could easily get expensive. They prefer a sort of cartelization in which each network has its territory, and dominates it.