I don't see how this could possibly work as you hoped, they will have load sharing based on stiffness and deflections, not to mention if it's an existing PT slab, you would have a re-distribution of forces due to new supports which will affect tendon placement. I see the following possible solutions:
1. Add FRP for the added moment, this requires analyzing the existing slab and the new and figuring out the additional required capacity.
2. Add a steel structure on top of the slab that keeps all loading off said slab, this will be tricky due to floor heights and support locations.
3. If it's a new slab, just design it for the new loading.
4. Analyze the existing slab, with the new beams, find a way to make them composite with the slab, and maybe there is a chance the tendon locations will work as is.