There's a utility called dfterm3 which is capable of co-op multiplayer, essentially letting you and a friend both have input and share a view over the web in real time. This would probably be enough for OP's request.
Why does everyone think that turn-based gameplay is a problem. That's nonsense.
It isn't a problem at all when two players are playing on one fort, the pause simply stops the game for both of them and both of them can continue giving commands in that time.
dfterm3 - multiplayer is decent fun already, if the lag/crashyness issues are any better than when I last tried. It would be much more fun, if multiple cursors, i.e. multiple simultaneous inputs were possible. Then we could have true collaborative building. The menus would pause, sure, but the players would have to agree on that themselves. But that would require a rewrite of how DF handles keyboard/mouse inputs, and would be useful only for that type of gameplay. For more extensive rewrites, some of the pausing menus could be changed so that players would choose whether they pause while browsing or not. I'm assuming that many menus require the game to be paused when you e.g. add or delete jobs (be they designations or workshop jobs) and such, but even if that's true, it could be possible to browse the menus without pausing, then when the command is given by a player, do a quick (automatic) pause-issue command-unpause. If that's too laggy, collect commands into a buffer like DwarfTherapist does. Would be really fun though, to have multiple simultaneous overminds on a single fort, instead of the current multiple personalities fighting for control in one overmind that dfterm3 does at the moment.
As for the "multiple forts in the same world" type of multiplayer, possibly with caravans, raiding parties, patrols, military assistance expeditions (to help lift sieges), stuff like that... well, that could be interesting. If caravans are set to happen in a fixed season each year, you could e.g. make the decisions about the caravans before the end of spring (assuming autumn caravans for dwarves like now), and then the world would be synced at the end of spring. That would allow each player to play out a 1-year "turn" at their own pace, before syncing has to be done. This would be similar to a play by email type of strategy game (e.g. The civilization franchise), except the "turns" of 1 dwarven year aren't played around the table by each player, but simultaneously, and then they're combined in the "end of turn" processing (there have been at least tactical turn-based games that handle combat like this. You either tell your guys to shoot in some direction as suppressive fire/because you assume enemies will be coming from there, or use some kind of overwatch mode, where they shoot on their own initiative if they see the enemy). For 2 player games there isn't much difference, btu the latter approach makes it much easier to increase the player count without vastly increasing the time you have to wait for your turn again. Heck, with the coming retiring AI, you could even give an ultimatum that if people don't play their turn on time, their fort will be handled by handled as being retired for that year.
This would still require splitting the world-advancement processes from the regular fortress gameplay stuff in a way that's probably different than what's being done at the moment/in the next patch. E.g. at the end of turn, you'd probably have to predetermine what migrants, sieges, megabeasts, FBs, animals (if any populations are shared between the forts), possibly caravans, and so forth, all the players get the next year, so you don't get a historical figure attacking/migrating to 2 different forts. Caravans are a possibly because currently they just come and go from thin air, but that's set to change; once traded items are tracked in even an abstract way, the stuff they bring to the fort would have to be generated in at least that abstract way, e.g. X food, Y weapons supplies, prior to any caravans "setting off" towards the forts.
For the military-type stuff mentioned above, we'd have to wait until the DF version that adds sending out patrols/counter-raids against goblins, anyway (AFAIK, planned but little or no timeline features). To be able to do this sort of thing at any time, you'd need to keep the world synced much more often than 1 year, but you could maybe also give orders for the whole year in advance. Or for a slightly more frequent interval that still allows some independent play time for people, once a season or once a month syncs. Imagine all forts are at least 2 weeks away from each other (for one sync per month). The communications delays would also make things more interesting, if you have to employ dwarven couriers to send messages etc. Extra points if the couriers and armies (patrols etc.) actually travel to the destination on the map, thus taking longer to get to faraway forts, and extraextra points if they can get attacked/obstructed on their mission. The army movement stuff is already coming in the next version though, so that isn't a big problem.
The above 2 variants, or some slightly more developed versions of them, are I think the closest to multiplayer DF that we could sensibly get without making it a vastly different game. But as mentioned before, Toady has expressed no interest in doing any kind of multiplayer. I think the systems I roughly laid out above
might still be possible a few versions/years from now if the external plugins and such would advance enough (especially the armies stuff needs a few releases), and definitely possible (though not assured to happen) if the DF source code is ever released. Which is going to take at least a decade, and probably several decades (until DF is ready and/or official development stops).