I am a licensed contractor in NYC and Nassau (disclosure:I am also a real estate broker in NY State).
If your plans are done and filed with Dept of Buildings NYC, then you wold need to get permission from the coop / condo board to proceed with your construction. Once all the aforementioned is complete you would hire a contractor to pull permits. Generally speaking the contractor will use a plumber with whom he/she is familiar with and that company would cover your plumbing permits. At that point you can proceed with construction.
If you have any further questions now or in the furture, feel free to contact me.