Your neigbours that have done it already will have the contractors, carpenters, debris crews, electricians, plasterers, painters that already have done it.. they'd probably love to tell you about how it was tackled, that would be the best route... have an under the roof party get to know everyone?

I'd cut a test hole to see if you really do have a full wonderful ceiling up there or if any plumbing etc. is in the way, you never know? You may have the side with damage and the reason why they covered the whole thing to begin with?

Thanks! Yes -- our neighbors have had the work done by contractors... do you think that this is a project that can be done by a homeowner? I was thinking about just knocking out the ceilings... what are your thoughts?

You may already have and be propagating a serious danger to all inhabitants of this building. If this is located in any city or town with codes enforcement, it will be an illegal situation.

Multipole family housing needs fire walls and firestops that will prevent the spredd of fire. The plaster was serving that purpose. Removing it puts everyone in the same strreucture at greater risk, should a fire ever occour.
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In the event that anyone ever loses their life or is injured due to this possibility, I don't doubt that lawsuits and possibly criminal charges would be brought against those who did such work, owners and contractors alike.

Check with city hall first.
I am not in any area with code restrictions like this but i would have serious moral reservations about such work.

As for other issues to consider, removing a ceiling to expose the beams exposes the utility runs that the dropped ceiling might conceal or contain: electrical, plumbing, cable or phone. Removing it might make the electrical work no longer meet code. For instance, they could have used sheathed electrical cable wire for the electrical runs, which is Code if covered by drywall or plaster, but is not Code for exposed runs. You would need to re-route the wires or have them re-run with THHN wire through metal conduit. I did it, myself (re-routing some runs through the walls and running others through conduit), but it was a significant task. It added far more work than merely ripping the ceiling out and finishing the beams.

As for fire protection, I doubt that the plaster ceilings served as fire protection required by Code, especially if the previous removal work was done by legitimate contractors. I wouldn't ignore the possibility, and it is something to consider and look into, but I also would not be so alarmist.

Moreover, you can do retrofit work that serves the same purpose. I removed my ceiling to expose the beams, which exposed gaps that led to the space above my neighbor's ceilings. I fit vertical, custom-fit pieces of drywall inside the beams where they met the walls (continuing the walls up inside the beams) so as to create a firewall in each gap between the beams. (There is also concrete above the beams).