The problem with your OU and UT scenario is that it may be tough for UT to go anywhere without TT and for OU to go anywhere without OSU.
Also interesting that OU would be at the very bottom of the academic rankings in the Big10 and are not a AAU member. Of course, Nebraska currently is the lowest ranked and is now without AAU membership. Seems some of those 'givens' on what you need for Big10 membership may not be so set in stone.
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