This Undertale mod adds local co-op, but playing online requires some extra work
Undertale Together allows for "couch co-op" out of the box and online play through a virtual desktop.
Originally released in 2019, Moddb user Depa31's Undertale Together allows two players to complete the entirety of Toby Fox's 2015 indie adventure, well, together. With help from a remote desktop tool like Parsec, it can effectively offer online co-op as well.
The mod itself is a pretty simple tweak to a lean game—you're able to name two players at the start and select overworld and battle sprites for the second player. One character is controlled by the arrow keys, and the other with WASD. Installation is an absolute breeze, with a .exe installer taking care of things in seconds.
Both players have their own health bar, and I could see the added action per round making fights significantly easier, though I could also see some emergent competitive play—a violent player sabotaging a pacifist one say, or vice versa.
Remote desktop software like Parsec, Anydesk, or Team Viewer can let a far away co-op partner take up one of the inputs like they're right there with you. This style of online play is often offered within games through Steam Remote Play, but that's a feature that has to be enabled by a developer—an external program's the only way to go with Undertale.
I didn't have the chance to test the mod with a remote friend, but I can confirm that it fully works as intended locally, with me operating both Fritzes at the same time like some kind of ascendant gamer. My previous experience with Remote Play left a lot to be desired—one or both of our internet connections were not up to snuff—but if you've got a robust connection or live in a country with actually decent infrastructure, using something like Parsec to play this online shouldn't be too much of a problem.
This wouldn't be how I'd recommend going through Undertale for the first time—it's a really narrative, emotional game—but Undertale Together is certainly a fun way to revisit a classic. It's less of an intensive project than the recent Skyrim co-op mod, but it's still a cool, sharable reinterpretation of the game.