In my experience in the life science, Dawn's answer is mostly correct. I have heard about different grants paying students more through RA positions in the life sciences depending upon the funding source, although this is rare. I would also add that some program give extra "scholarships" or "fellowships" to better students. For example, Texas Tech (where I went for grad school) has scholarships for grad students and I was able to receive merit-based scholarships on top of my departmental stipend or external fellowship during different parts of my graduate eduation.
Texas Tech also previously had an ARCS Foundation scholarship and these awards were on top of existing support from Texas Tech. I mention this because Seattle (where the University of Washington is located) also has a chapter of the ARCS Foundation and you might be able to apply there for additional funding. I do not know how the Seattle ARCS Foundation works or if you meet their other requirements.
Lastly, I have heard that some Universities that give "bonus" scholarships to people who obtain supplemental fellowships as well as some advisors who give "bonuses" for students who publish (e.g., $500 per paper). I do not have links for any of these, only second-hand accounts. Both of these seemed to be rare and from well funded universities and professors.
To include other examples from the comments:
- From Dawn: I can confirm- in my PhD institution, we received a “bonus” in our research account if we got an external fellowship. It could be used for travel or materials or books or experimental subject payments, etc. but not taken home as salary.
- From Brian Krause: Another "bonus" method in my grad program was that students paid by fellowship or traineeship were not subject to paying the "segregated fees", which were about $1000/year and were not ordinarily covered by tuition remission.
Edit: I also missed your original question: Also, are negotiations acceptable in CS in USA?. I do not know about CS. For life science, I have seen people match other offers, but very rarely. You might gently ask if a program could match another program's offer, but I defer to people who have gone to grad school for CS.