I have three recommendations.
Split Fiction is a master class in game design. The split screen is so integrated into the experience that even online multiplayer is in split screen. The screens are a part of the story.
The gameplay is constantly changing to the point that discovering new mechanics becomes the gameplay loop.
The level designs are so clever that you'll have several moments that feel scripted but were actually just inevitable because of how we play games.
To give a snapshot of the experience: there was one scene where my character was driving a motorcycle along the sides of skyscrapers, doing the craziest stunts imaginable, and my wife's character was sitting on the back frantically trying to solve a series of CAPTCHAs on her phone. She was so focused on keeping a steady hand that she barely noticed the death-defying stunts happening literally out of the corner of her eye.
By the end of it I was like, "Did you see that??" and it turns out she did not. It was absurd and hilarious, and it's the kind of storytelling that only works in a video game.
My current obsession is UFO 50, which is a collection of 50 "retro" games. In real life they're all new, but the story of the game is that they're from a company from the 80s called UFOsoft, and then there's a dark meta narrative hidden in the background.
Which is all just a framing device for 50 games, most of which are good, some of which are amazing, and half of which are couch co-op multiplayer. It's like exploring the Switch's retro NES collection for hidden gems, except there's a lot more gems.
There are beat 'em ups, obscure sports games, some platformers, tactics games, a little bit of everything.
I've enlisted my wife to help me, because a lot of these games are just begging to be grinded out in co-op.
I got the game when I saw someone describe it as "a master class in game design", and I thought, "that's the phrase I've just been using to describe Split Fiction."
And finally, I recommend Lovers in a Dangerous Spacetime, because that's the multiplayer game I've been recommending for almost ten years.
You each play as adorable creatures in an adorable space ship that you customize as you go. The ship has several stations that need to be manned, including the captain's seat, navigation, a directional shield, and multiple weapons.
But you each can only man one station at a time. So if you need to stay on the shield but a new enemy is approaching from the other side, then that means the captain is going to have to jump on a weapon and leave the ship adrift.
You may have arguments over which type of weapons to add to your ship or over who's better at piloting which kind of engine. Or maybe you'll work together in perfect harmony, relying on each other's strengths and covering each other's weaknesses as you adapt to every new challenge. Both ways are fun.
Also great for up to 4 players.