ZDoom

No, that can't be done. Especially your example won't work because it would cause immediate desynchronisation in a multiplayer game. There is a good reason why the state of all machines has to be the same. Collision detection is a tricky thing and errors are cumulative so even if you don't notice it at first after some time it will show.

I have no idea if this is even in the realm of possibility. I'm more floating an idea than making a request, really.

Would it be possible to add a "desync" flag to specials that would allow them to occur only for the player that activated them, and not be reported to other players?

As for why in the world one would want this, it would be useful when creating special effects that don't have an impact on gameplay, only appearance. (Specifically, I have a half-underwater platform that is made to look solid by moving the dummy floor down when the player drops underwater, and up when he rises above it. This obviously breaks in multiplayer.)