Update: A Chucklefish representative tells me that multiplayer won't ship with the Switch version of Stardew Valley that's releasing this summer. "PC users will still get to check out Stardew Valley multiplayer first," says Chucklefish's Molly Carroll, but that update won't be ready in time for summer, either. "It'll take some more time to get multiplayer where we want it to be!"
Sorry to dash any hopes—it's my fault for misunderstanding the Nintendo announcement to mean that the Switch launch this summer would include multiplayer. The original, now out of date, story is below.
Eric Barone released Stardew Valley as a singleplayer game, but only because multiplayer support wasn't finished yet. So we've known for a while that multiplayer is coming to Stardew Valley—officially, that is—and today it's been revealed that the big patch may be coming this summer. But we're not completely sure yet.
Nintendo announced today that the Switch will be the "first console" to have Stardew Valley multiplayer when it releases for the system this summer. As "first" is qualified with "console," the multiplayer update could come to PC at the same time, or even earlier—though nothing about it has been announced explicitly.
The last we heard about multiplayer was on February 7, when Barone wrote: "All we can say is that we’re working on [multiplayer] and making progress. It’s not ready yet, though, and we can’t give you an idea of when it will be. We’ll let you know more as soon as we can. Sorry for making you wait!"
I've reached out to clarify whether or not PC multiplayer will come along at the same time as the Switch release, and will update this article if I hear back.