(This ended up being a lot longer than I expected, and parts of it might not make sense. I'll edit it when I get a chance to make it more readable. Most of it's just hypothetical, so don't take it too seriously.)It
might be possible (but very complicated) - the simplest way I can think of is to keep track of which screen and location each player is currently viewing, and switch to it (in DF) whenever the player interacts with the web interface (for only a frame or so, long enough so it can be rendered and sent to the player). It's definitely not easy (or possible, with the amount of time I don't have
), and there would probably be performance issues with constantly switching back and forth between screens. Timing issues would be even worse - it would need to keep track of which events correspond to which screen, and multiple players sending rapid sequences of keys (or worse, playing back macros) would either require some heavy buffering or cause a lot of lag.
This actually sounds like an interesting idea, now that I think about it. If only I knew enough C (I could always try Lua or Ruby, but I doubt they would be fast enough for this kind of thing).
Keep in mind that the only thing this could possibly work for is performing two unrelated or non-conflicting tasks simultaneously - for example, setting up a squad and assigning a noble at the same time. Designating in different areas might work too, but doing it in the same area would probably cause conflicts (since players' designations could overwrite each other). Maybe even crashes, in the case of constructions - for example, if player A selects a location for a wall, player B selects the same location and a material, and then player A picks a material, DF might try to place player A's wall without checking and crash (I haven't tested this yet, so DF could perform checks to prevent this from occurring.)
Of course, this would rely on a way to switch between views quickly. The screen position should be fairly easy to control, but I don't know if there's a way to switch directly between, say, the manager and status screen with DFHack. An alternative would be to record the keys the player uses to get to the relevant screen and play them back to access it again (that wouldn't work for everything, though, since there's a risk of repeating things like designations, but maybe you could only record keys that trigger a screen change).
Another thing that just occurred to me is pausing. It would probably be a good idea to only let the game run unpaused if no players are using another screen (for one thing, it would be annoying to have dwarves digging out an area you haven't finished designating, and for another, game progress would slow down if the game has to switch between screens as well). On a related note, nearly every screen would only require redrawing on a keypress (except for the main fortress mode view), so that might make things a little easier/faster.
So yeah. It could potentially be possible, although it would require a lot of work (and time) to make it happen if it were possible.