I'm replaying the Solo Mode, and right now it's me (Luigi), Mario and Yoshi vs Magikoopa in Bob-omb Factory. As far as I know, here are the matches that can come up. I'm sure that they can happen in any stage as well, so it can be 2 CPUs vs you on Toad Road. (Don't think that will ever happen though)
1 vs 1
2 vs 2
1 vs 3 (you on the team of three)
1 vs 2 (you as the solo player)
1 vs 2 (with a CPU ally)
1 vs 1
2 vs 2
1 vs 3 (you on the team of three)
1 vs 2 (you as the solo player)
1 vs 2 (with a CPU ally)