I like the 3-6 format where each school has 3 permanent opponents each year and rotates through the other 6 teams home/away every 4 years. In the comments someone posted an example of how this would look. I think Andy Staples of The Athletic did something similar many months ago.
"My stab at permanent opponents. I tried to balance historical rivalries, regionality, competitiveness, and more recent rivalry. No one is going to be completely happy, but the beauty is you still play everyone else twice over a four year span.Alabama - Auburn, Tennessee, LSUArkansas - Texas, Missouri, Texas A&MAuburn - Alabama, Georgia, Miss StateFlorida - Georgia, South Carolina, KentuckyGeorgia - Florida, Auburn, South CarolinaKentucky - Vanderbilt, Tennessee, FloridaLSU - Texas A&M, Miss State, AlabamaOle Miss - Miss State, Oklahoma, VanderbiltMiss State - Ole Miss, LSU, AuburnMissouri - Arkansas, Oklahoma, South CarolinaOklahoma - Texas, Missouri, Ole MissSouth Carolina - Missouri, Georgia, FloridaTennessee - Alabama, Vanderbilt, KentuckyTexas - Oklahoma, Arkansas, Texas A&MTexas A&M - Texas, LSU, ArkansasVanderbilt - Tennessee, Kentucky, Ole Miss"
The Athletic article: