Yes, yes, cooperative multiplayer already exists for The Elder Scrolls. It's called Tamriel Unlimited, which launched a couple of weeks ago (at last) on consoles. Yet for those who wish the same thing was possible within The Elder Scrolls 5: Skyrim, there's this, a mod for the PC edition of the 2011 game.
It's called "Tamriel Online" and, full upfront warning, its maker says he hasn't tested the thing beyond fooling around with a friend. "I can't really confirm that there's no horrifying problems until I've gotten some more feedback," says Redditor Siegfre, which means it's possible horrifying problems do exist. He's looking for others to help test it out before pushing the mod into a general release.
In fact, he's already solved crashes on death, and in-between loads after users pointed them out. Other volunteers have been able to confirm that Tamriel Online works with more than two cooperative players. So the crowdsourced testing, while it doesn't warranty a clean experience right now, has helped nudge the mod along toward better things.
To be perfectly clear, major gameplay features — such as combat — are unavailable in the present build (creatures or NPCs attacked by one player will not show up for the other; Siegfre intends to address this). Right now it's useful mainly for cooperative exploration.
YouTube's Brodual gives a solid overview of what the mod can and cannot do in the video above. "There's something quite surreal about running around Skyrim with an actual living person," he says, noting that development on cooperative multiplayer mods for the game have stretched back as far as 2012.
Instructions for downloading and applying the mod are at this link but, fair warning, do not expect a smooth or fully featured experience with this build. For those looking for a diversion or a proof-of-concept, though, it should be enough to tickle their fancy.
Here's another video, by YouTuber nateplays: