How do I turn a seized SS screw in a brass fixture?
First I would hit the screws with a penetrating lubricant like PB Blaster or Kroil. Then I would make sure that I have the absolute best fitting phillips head bit on the end of my screwdriver. Then I would push into the screw driver with all my might while slowly turning counter clockwise, and cross my fingers that it does not strip. And then if they do strip, then you have some options:


cut off the head of the screw. I don't know exactly what your situation is, but many times the head of the screw is what is holding the things together, so cutting it off will eliminate the pressure. Once things are taken apart you'll have a threaded rod stuck into whatever it's threaded into, but if enough of it is exposed then you can use a vice grip to get it out.
drill out the screw. This would be difficult on something like stainless steel, and you would also ruin the threads of whatever it's screwed into (if it's a nut then no worry). 
cut the head of the screw into a square or something to get a socket onto it. Will be too hard if it's a small screw
blast away the screw with a torch. Something tells me this would be inappropriate for your situation
use a screw extractor socket. I have had good luck with these. 


If breaking the head off the screw would compound your problem further because you will be unable to get the threaded rod out, then you're biggest priority should be not to break the screw! If this happens, then a machine shop may need to mill it out.