There are a ton of possible permutations, even after you get in all of the most necessary games.
But in pretty much all of my 3 rivalry scenarios, the following games pretty much always exist because by feel, they seem to me the games that most need to happen.
Alabama-Auburn
Alabama-Tennessee
Auburn-Georgia
Florida-Georgia
Georgia-South Carolina
LSU-Texas A&M
Ole Miss-Miss State
Missouri-Oklahoma
Oklahoma-Texas
Tennessee-Vanderbilt
Texas-Texas A&M
After that there is a group of games that fall in to place pretty much every single time, whether through the existence of a secondary rivalry or a necessity of geography.
Alabama-Miss State
Arkansas-Texas
Arkansas-Missouri
Auburn-Florida
Florida-South Carolina
Kentucky-Tennessee
Kentucky-Vanderbilt
LSU-Ole Miss
That leaves the following spots that are usually the ones that are shuffled around in many ways. Each of the following school still has an open game.
Arkansas
Kentucky
LSU
Ole Miss
Miss State
Missouri
Oklahoma
South Carolina
Texas A&M
Vanderbilt
So theres really quite a lot of ways that could go. For example...
Alabama: Auburn, Miss State, Tennessee
Arkansas: Ole Miss, Missouri, Texas
Auburn: Alabama, Florida, Georgia
Florida: Auburn, Georgia, South Carolina
Georgia: Auburn, Florida, South Carolina
Kentucky: Miss State, Tennessee, Vanderbilt
LSU: Ole Miss, Oklahoma, Texas A&M
Ole Miss: Arkansas, LSU, Miss State
Miss St: Alabama, Kentucky, Ole Miss
Missouri: Arkansas, Oklahoma, Texas A&M
Oklahoma: LSU, Missouri, Texas
South Carolina: Florida, Georgia, Vanderbilt
Tennessee: Alabama, Kentucky, Vanderbilt
Texas: Arkansas, Oklahoma, Texas A&M
Texas A&M: LSU, Missouri, Texas,
Vanderbilt: Kentucky, South Carolina, Tennessee
-or-
Alabama: Auburn, Miss State, Tennessee
Arkansas: LSU, Missouri, Texas
Auburn: Alabama, Florida, Georgia
Florida: Auburn, Georgia, South Carolina
Georgia: Auburn, Florida, South Carolina
Kentucky: Missouri, Tennessee, Vanderbilt
LSU: Arkansas, Ole Miss, Texas A&M
Ole Miss: LSU, Miss State, Vanderbilt
Miss St: Alabama, Ole Miss, Texas A&M
Missouri: Arkansas, Kentucky, Oklahoma
Oklahoma: Missouri, Texas, South Carolina
South Carolina: Florida, Georgia, Oklahoma
Tennessee: Alabama, Kentucky, Vanderbilt
Texas: Arkansas, Oklahoma, Texas A&M
Texas A&M: LSU, Miss State, Texas
Vanderbilt: Kentucky, Ole Miss, Tennessee
-or-
Alabama: Auburn, Miss State, Tennessee
Arkansas: Missouri, Oklahoma, Texas
Auburn: Alabama, Florida, Georgia
Florida: Auburn, Georgia, South Carolina
Georgia: Auburn, Florida, South Carolina
Kentucky: Missouri, Tennessee, Vanderbilt
LSU: Ole Miss, Miss State, Texas A&M
Ole Miss: LSU, Miss State, Vanderbilt
Miss St: Alabama, LSU, Ole Miss
Missouri: Arkansas, Kentucky, Oklahoma
Oklahoma: Arkansas, Missouri, Texas
South Carolina: Florida, Georgia, Texas A&M
Tennessee: Alabama, Kentucky, Vanderbilt
Texas: Arkansas, Oklahoma, Texas A&M
Texas A&M: LSU, South Carolina, Texas
Vanderbilt: Kentucky, Ole Miss, Tennessee
-or-
Alabama: Auburn, Miss State, Tennessee
Arkansas: LSU, Missouri, Texas
Auburn: Alabama, Florida, Georgia
Florida: Auburn, Georgia, South Carolina
Georgia: Auburn, Florida, South Carolina
Kentucky: Miss State, Tennessee, Vanderbilt
LSU: Arkansas, Ole Miss, Texas A&M
Ole Miss: LSU, Miss State, Vanderbilt
Miss St: Alabama, Kentucky, Ole Miss
Missouri: Arkansas, Oklahoma, South Carolina
Oklahoma: Missouri, Texas, Texas A&M
South Carolina: Florida, Georgia, Missouri
Tennessee: Alabama, Kentucky, Vanderbilt
Texas: Arkansas, Oklahoma, Texas A&M
Texas A&M: LSU, Oklahoma, Texas
Vanderbilt: Kentucky, Ole Miss, Tennessee
etc