I did plaster ceiling with the beams visible in in the living room, dining area, car porch and kitchen. I just lowered the ceiling a little bit sufficient to fix the led down lights. I didn't fix a plaster dome as this would require the ceiling to be lowered even more. There is cornice At all sides. Living room and dining has a simple box design and the original concrete ceiling is maintained at the centre but it's plastered ( to make it look as if it's a plaster ceiling and each of the 4 side is boxed. The result? Although the beams are still visible, it still looks good. It's a simple and elegant design. I do not feel claustrophobic as the ceiling is still high. My suggestion is not to lower the ceiling and conceal the beams especially in  houses where the original ceiling height is already  low and made worse with many beams which are very low such as in my situation.

Purpose of plaster ceiling is to have it cover the beam.

Maybe I correct my earlier comment;

plaster ceiling to to have a nice ceiling home owner like. If having a plaster ceiling and still expose beam and home owner still like it than is ok.

Many homeowner prefer to hide beam and have a flat ceiling. Some homeowner maybe different.

height of the plaster ceiling? answer is very clear, ask high as possible. and just like other member say to cover all the beam, wiring, aircond and many other.

As you say, your plaster ceiling after beam is only 8.5ft? not really a problem actually, you still can maximum the height, how? for example, making some design like light box to higher up the living hall ceiling at the center part, but remain the side high to the beam height, then you will have the higher ceiling at the main activity place, do it the same to your dining hall, then everything will be find already

Where possible leave as much ceiling void for comfortable heat stratification - proper separation of hot layer of air from the cool where the body doesn't perceive it. For 10.5' ceiling they would be about 9.5'-10' net ceiling space.

Plan how the AC pipes, electrical, comms (RJ11 (phone/fax), Cat5/6LAN, Fiber, RC6, HDMI, Security camera comms) will be conduit-ed.

Plan where your fans would be since either ceiling hooks needs to be pre-drilled or if there's no ceiling hooks, they'll use wood affixed to plaster ceiling structure. If rooms are large, 2 small-medium fans better then 1 big fan. Plan ahead like where occupants center would be. Well placed fans relative to occupant activity works best than a room centered fan which doesn't reach anyone at all.

Allow 3-4"clearance below the beams only and expand the minimally until where required e.g. ceiling AC (min should be 11ft ceiling) which should be near the beams to minimize eating up valuable ceiling void.

Allow for 6-12" from ceiling for box lighting and fan. Slightly more if ceiling AC are used but now newer ceiling AC models requires less clearance then before. Only limiting factor is beam height.

Plan the manholes to access electrical & comms junction points and/or ceiling AC maintenance.

3-4" clearance below beam allows for LED downlight, more e.g. 6-8" for compact fluorescent light.

In your case, if beams are too low, then surround perimeter and beam only up to 3-4". This leaves a rectangular void that allows for  proper heat stratification else if too low 8.5ft, one feels perpetually hot and humid. Minimum net void height would be 9ft but generally I'll go for 9.5'.

Something for you to compare TS. My ceiling is 9.8 feet. I'm 1.72m tall. With a ceiling fan, things are just nice.

The ceiling fans always installed on the concrete ceiling - never on a plaster ceiling.
It just passes through a hole in the plaster ceiling.