Just announced today is a new non-conference series: Mississippi State and Arizona are going to play a home-and-home. The game will be in the desert in 2022, and the followup in StarkVegas coming in 2023.
It's important for Mississippi State to line these games up thanks to the new non-conference requirement of playing at least one Power 5 conference game per year. MSU has complained in the past about having a hard time lining up such games because teams from other conferences don't like coming to Starkville, and it is one of the few SEC teams not to schedule a P5 team with regularity of late.
As for an SEC team playing Pac-12 teams, it's not as uncommon as you might think. Between 2006-13, current SEC members played more regular season games against Pac-10/12 teams than any other conference except the ACC. It wasn't a result of a bunch of neutral site games, as only LSU-Oregon in 2011 was one of those.
One wonders whether both Rich Rodriguez and Dan Mullen will both still be around when the games will occur, given the rapid churn rate of coaching. Mullen owes a lot to Rodriguez philosophically, so it'd be a great matchup to see if both are still in their current posts. Eight years is an eternity in college coaching, though.