Miliastra matching, need infinite matching queue

We need to be able to queue up for matching in multiple games at one time. Like, sure, I'm interested in playing game #1, but would rather play any game at all with someone, and I'd also like to play games #2-#n just as much.

I don't know how to nail down the timing exactly when someone else out there in the universe wants to play one of the games I'm interested in. Say I match for 20 minutes on game A, and someone else wants to play game B during that time, I already missed them. When I finally give up after 20 minutes getting no matches for game A, and start matching on game B, too bad, now no one is queueing up for game B, because I already missed them. We're not suffering from having too many players clamoring for multiple stages, we're suffering from too FEW.

tl;dr The mode would be way more fun with more efficient ways to match other players for games