These are games that have two things at once: 1) a single player mode, and 2) a multi-player mode that's fleshed-out enough that T and I might enjoy playing it together.
The strategy is this — There are a LOT of games on Steam. Too many. To cope with that, we will 1) locate games that are single+multi, 2) one of us will do a "trial run" to evaluate each game in single-player mode, and 3) if it's a game that individual likes, then they will recommend it as something that we might play together.
NOTE that some Steam games are tagged with "multiplayer", but are not actually multiplayer! I believe tags are user-generated, and can sometimes be made in error. It's a good idea to double-check that a game actually has a multiplayer mode, and that the multiplayer mode is sufficiently fleshed-out enough that we would enjoy it.
(One example of this is "A Short Hike". In this case, it used to have a multiplayer mode, via a mod that the original author created. However, that mod now bears the warning "The server for this mod has been taken down. It is possible to spin up your own server, but that is for advanced users only." In this case, I consider the "multiplayer" tag to be misleading and not wholly accurate.)