Local coop, I assume? Three games come to mind.

• Gauntlet 2014 is a top-down hack'n-slash with light puzzles. It's slick and solid in everything it does, and coordinating your spells in coop improves the experience tenfold. The classes are varied enough that everyone should have fun with it.

• Lara Croft and the Temple of Osiris is a twin-stick isometric shooter, but on top of the regular action / combat, you also get tons of very clever cooperative puzzles that make use of everyone's special abilities. If you know Lara Croft only from the flagship games, don't dismiss this one as a cheap spin-off, it's actually a solid game in all regards.

The previous game, Lara Croft and the Guardian of Light, only allows two players.

• Helldivers also supports four players on the same screen. This time puzzles are nowhere to be seen, it is an action game with tons of great mechanics (no top-down shooter "feels" as good, save for maybe Alien Breed), inevitable situational humor and fuck-ups, and all in all a huge lot of fun. Be warned though, unlike the two previous examples it doesn't have a campaign, it's a hub-based multiplayer game: select a map, complete it, return.

Both Helldivers and Gauntlet are from the creators of Magicka, which should quickly be obvious considering the levels of polish and accidental humor from friendly fire and fuck-ups.

As for 3-player local coop, Gears 5 got released last month, though I fear it's a bit of a shame to play that without decent familiarity with the other games of the series. If that's not a problem to you, then here goes: two players control regular human characters, the third controls a robot who has more of a support role though it's still a great experience, you don't feel like a second fiddle at all.

Gears of War 4 (and all previous games on consoles) only allows two players.