If the Big East is ever going to have any stability, discipline must be invoked.
There are several Big East schools wanting to join B1G, Big 12, ACC, or SEC. Some have announced their desires.
Some schools are making manipulative moves such as reestablishing old rivalries or creating new ones with programs in other conferences. When this is done simply for out-of-conference games, no one can complain. When it obviously in hope of creating working relationships for future moves, that is an entirely different story.
If an increased number of schools actually happens, the commissioner may have more control.
I once worked for a retired military man. If an employee entered his office with an issue he did not think was in the best interest of the organization, he would simply say "I accept your resignation".
Perhaps, the new commissioner could do something similar. As example, if a school publicly states an interest in joining another conference, that is detrimental to the other schools in the conference. It could diminish media contracts, bowl agreements, stature of the remaining schools, etc. In that situation, the commissioner should simply say "We accept your withdrawal from the conference. We will make sure your name will not appear on the schedule next season".
That would work for the benefit of every school except those that think they are better than others, when they clearly are not. Such a school is acting to the detriment of the conference and its members. The school establishes itself as undesirable.
All such a policy asks is for schools to be a little discreet in their public statements and activities. Other than that "don't let the door hit your sorry ass on the way out.