I think you get pods instead of divisions once you get to 16 teams. And it could be ugly looking but work.
Oklahoma-Texas-A&M-Arkansas
Missouri-LSU-Ole Miss-State
Alabama-Auburn-Vandy-Kentucky
Florida-UGA-UT-SCar
OR
LSU-Florida-Texas-A&M
UA-AU-UGA-SCAR
OleMiss-State-Oklahoma-Arkansas
Missouri-UK-Vandy-UT
Each team plays their pod every year, one other pod (rotates over 3 years), and then a rivalry game. That is either their standard rival (UT in our case) or another rival from a different pod if we are playing our rivals pod that year (LSU for us maybe). That gets you 8 games a year. If you stretch to 9 games then you can add another rivalry game to the mix.