Assemble a team of three
The Cave is an adventure game from Double Fine Productions, created by Ron Gilbert. You pick three characters out of seven, and the group descends into a large, seamless cave-world. The seven include a Hillbilly and a Time Traveller, and each one has their own personality, special talents, and a dark, secret reason for going down there. The cave itself is not a normal cave: you will come across a subterranean amusement park, a medieval castle, and a fully armed nuclear tipped ICBM that is ready to launch.
Playing together
The three characters are switched between as you go, and the puzzles are solved by using their different talents together. The game supports local co-op, so friends can share the exploring on one screen. Physical puzzles and classic adventure puzzles both show up, and the humor runs dark. Steam also lists Remote Play Together, which lets people join in over a connection.
Before you start
Each character carries their own story, so a new set of three opens up different story beats, puzzles, and areas of The Cave, along with hidden treasures and collectables. The treasures are not redeemable for cash. The game is tagged as a 2D side-scroller with point-and-click elements and controller support, and it is listed as playable singleplayer as well.