Thinking about it a little more, the original Big 12 could have been set up with a divisionless format where everybody got 5 permanent rivals and played everybody else 50% of the time. The permanent rivals could have been
Neb - OK, Col, ISU, Kan, KSU
ISU - NEB, Mizzou, Kan, KSU, Bay
Kan - NEB, KSU, ISU, Mizzou, Col
KSU - Kan, Neb, Col, ISU, Mizzou
Col - NEB, Kan, KSU, TT, OSU
Mizzou - ISU, Kan, KSU, OK, A&M
Ok - Tex, OSU, Neb, Mizzou, Bay
OSU - OK, TT, Col, Tex, A&M
Tex - OK, A&M, TT, Bay, OSU
A&M - Tex, TT, Bay, OSU, Mizzou
TT - Tex, A&M, Bay, OSU, Col
Bay - Tex, A&M, TT, ISU, Ok