OU's most-played OOC series against opponents not currently in the Big 12:
Missouri, with 96 meetings. But most of the games--all from 1928 onward--were conference games.
Nebraska, with 86 meetings, 7 as OOC opponents, 1 as bowl-game opponents although both were in the Big 8.
59 games with Colorado, 55 as conference-mates.
28 games with Tulsa.
15 games with Arkansas, but only 3 since 1926.
11 games with Notre Dame.
Maybe I'm missing some with more than 11 games played.