Would the total need to be an even number and a multiple of 4? 20 would work but there would be one 6 team division. I would think at that the right number may be 20 with 2 divisions and a championship game.ACC has 7 team divisions.
I would go real big, add two more divisions of 7 from the PAC12/Big12 remaining teams.
Then you can keep league play within the two eastern division and within the two western divisions.
Have a league football championship with the Coastal and Atlantic winner play and Pacific and Central winners play to play in the championship game, and all other sports have a 28 team playoff.