My favourites include (in no specific order) Crash Team Racing, Quake II, and Dynasty Warriors, and Worms Armageddon. Those are probably my favourites, and, as you can see, they're quite ancient. Local multiplayer on consoles isn't doing too well these days, I fear... I mean I guess there must be tons of great games, but they seem too much like 'party games' for my taste.
The Worms Franchise is amazing, they steered off a little bit but with the Worms WMD on switch I felt it was just like Armageddon. If you haven't played it I think you could have some fun with it. The multiplayer is amazing, and as a bonus there are all the solo missions that are fun as well.