the schedules are so random. So let's go with the 4 divisions below for football only. You play the 3 teams in your division and all 4 teams in one of the other 3 divisions, rotating crossover divisions every 3 seasons.

And then each team in your division plays 1 game against 1 of the 4 teams in another crossover division to get to 8. No games are played against the 3rd division.

At that point everyone has played 11 games with 4 home and 4 road conference games.

And everyone gets at least 1 more. 2nd, 3rd, and 4th place division teams play the corresponding 2nd, 3rd, and 4th place team in the division they didn't play. So they all get a unique opponent.

The division winners play semifinal games against the division winner from the division they didn't play.

And then of course you have the conference championship game for the winners.

Arizona
Arizona St
BYU
Utah

West Virginia
Cincinnati
UCF
Iowa St

TCU
Baylor
Texas Tech
Houston

Colorado
Kansas
Kansas St
Oklahoma St