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flat plate strengthening

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Does anyone have any advice on methods of strengthening a flat plate slab with drop panels in an existing hospital? We cannot likely remove any live load except from a very limited area. It may be possible to go underneath and place steel or additional concrete. I am dealing with spans of about 26ft and 20ft.
The slab is not working in negative bending at a column strip over the column (not enough top bars), punching shear is not a problem. It would work if there was more rebar in the slab initially... The building was built in 1960, we do have some of the original drawings and are working on getting additional drawings. We are adding about 9000lbs total of medical equipment to a room that works out to about 70psf, but the capacity we are getting thru calcs is about 50psf. I know that uniform load does not equal the effects of point loads, this is just the first step and quite a bit off the required capacity.
Though I have never done it before, if you could get a majority of the LL off of the slab, could you maybe cut the slab and epoxy/grout in rebar, or use carbon sheets for additional negative reinforcement? I am thinking the problem in our application would be that it would be necessary to add this outside of the room, out into the hallway...
Thanks in advance, please CC me directly.
Andrew Kester, P.E.
Principal/Project Manager
ADK Structural Engineering, PLLC
1510 E. Colonial Drive, Suite 301
Orlando, FL 32803