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'.
Thanks for the insight.