How many bays are there at the moment (sorry currently)?

You need to compare what the moment diagrams are going to be like before and after, if they are completely different then this is a problem, if they are within 10% of each other then you may be able to redistribute the moments according to the code.

You may need to put cantilevered sections at the edge of the openings to keep the continuity.

If I understand your plan correctly, it sounds like you will still have 2 columns in the middle, going up to more floors or the roof?  You might want to check those columns if they were braced by the slab you are removing.

Issues I see (summarizing the good points of PMR06 and csd72):

1.  Will columns extend past the removal floor and therefore have double or more unbraced length that originally used in design?

2.  Will adjacent slab areas that are not removed be now subject to higher positive moments due to loss of continuity from the removed slabs?

3.  Will partial floor removal affect the lateral force resisting system of the overall building by diminshing the compentency or size of the floor diaphragm?

4.  Will partial removal of the floor affect the fire protection plan of the building?  Many times concrete floors require a 1 hour or more separation between floors unless other actions are taken to protect the new open area.

Also, is this a flat plate/slab or are there beams at the column lines? If there are beams, then you need to calculate the torsion in the beams created by the unbalanced moment at the discontinued slab sections. If it is a flat plate/slab, the unbalanced moment will be resisted through shear and you will need to check the shear capacity of the slab, particularly punching shear near the columns. JAE, am I correct?

mitchelon - good point on torsion issue if there are beams.  Beams weren't mentioned in the OP however.

Punching shear at the columns would be a big deal - I'd probably want to hold the "cut" away from any columns -leave cantilevers like csd72 said.

I had a similar situation in a hospital where the owner wanted to install imaging equipment but did not have adequate floor-to-floor height.  The floor was a two way flat plate system with drop panels at the columns.  No beams.  I had drawings showing the reinforcing and framing.  The framing sizes were field verified (slab thickness, drop panel dimensions, column sizes) as well as some of the rebar.  JAE lists the things that I checked.

I had a school library with a flat plate where I specified concrete walls to the edge of the openings to maintain moment continuity.

Adjacent floor spans need to be propped from before removal of the floor till after the wall has cured. You also need to take into account that the new wall will creep, but the existing slab wont(as much).

You also need to specify that they expose a lap length of the reinforcement to lap with the wall bars.

This is an expensive option though.

I want to thank everyone for comments.  I will look into these.