IMO all 10 schools hold a lot of power when it comes to Big12 expansion. Obviously, Texas and OU hold the most power because if they both don't sign a GOR extension, I am not sure expansion happens.
When it comes to which schools are invited to join, then each school IMO has a lot of power. It only takes 3 to say no and there could be competing agendas. WVU might want to add eastern teams, UT + Houston politics, importance of academics in selection, etc
However, I think in the end, who gets the invite to join will be determined by the numbers- which group of 2-6 schools bring the most TV value based on what the Big12 sees the go-forward revenue model. Is there still a chance at a Big12 Network? Are ESPN, FOX/CBS/NBC Sports channels willing to bid on Big 12 content? Is the future Netflix, Amazon, etc?