In my opinion it would be tricky to share the design of a PT parking ramp with the supplier. It could work, but you would have to set up good channels with the supplier's PT engineer and preferably have them on staff prior to bidding the documents.
The main issue that I see you having are with the sharing of load between the columns and the PT slab. For example - the stiffer the column the more moment it takes into it, the less moment the beam has to take. And conversely, the stiffer the beam, the more moment it takes, the less moment goes into the column.
Now for straight gravity runs on square buildings this really isn't an issue because our friend the ACI allows us to assume moments of inertias for columns.
However, parking ramps typically have beams intersecting columns at locations with a short elevation change between them; which leads to very stiff columns taking very very large moments into them from the beams. These joints become a bear to detail properly.
Anyway, for your information this is how I do it:
1) Set up gravity runs with ADAPT or equal, my firm just purchased Concept, which is ramsteel's version of Floor2. (finite element analysis has become a major player in PT)
2) Set up lateral models including gravity and lateral (wind, temp and shrinkage) with Risa or equal. Input the column stiffnesses based on ACI modifiers to gross moment of intertia. Include secondary moments from ADAPT in this model - they will typically help your column design. Look for issues with columns taking too much load.
3) Take lateral loads from Risa and input into ADAPT. Watch out for the weak direction in one way systems (slab span perpendicular to beam direction).
4) "Play" between the Risa and the ADAPT models so that the moments correlate between them. At this stage remember to detail your column joints at the intersection of beams, these get conjested very quickly.
5) Pull final PT sizes onto drawings
6) Pull final column reinforcing onto drawings
7) Pull final slab rebar onto drawings.
Anyway, hope this helps. Let me know if you need more