Here are my thoughts. I think students can and should discuss the financial offers with schools when they need the additional money. I won't use the term "negotiate" because it's not really a negotiation. A negotiation requires both sides to have something the other wants and it is very rare that a student is in a position where the student cannot be replaced by another person the school has accepted.
However, schools that accepted you obviously prefer you over some other candidate. They aren't granting this offer out of charity---it's because they believe they are better off with you than someone else they didn't accept. So, if they have the ability, they could be willing to change your offer to make it more attractive to you.
This is the mindset you should adopt when asking for more money, in my opinion. It's not about negotiation like a job offer, but about making sure you get your needs met. Some professors will tell you to not ask for more money at all, or that you should be happy that you get an offer at all, but I think this mindset is outdated and harmful to students. It is my opinion that the school derives as much value form our work as we get from the education, so stipend shouldn't be a taboo topic. I believe that more students are talking about stipends today than in the past.
Now, that said, to answer your question: how to ask for more money? You need to first do your research. It sounds like you are worried about the cost of living at School A so you should find out actual information about the cost of living. The exact advice depends on the specifics of your situation (which you don't have to explain here). Note that most physics programs in the US will provide a stipend high enough to cover cost of living, so you usually need to have a special additional expense in order to make a strong case for why you need more money. If you just want more money for the sake of earning more then you can certainly try to ask, but I doubt you will be very successful.
However, if you have a medical condition that requires $2000 per year to upkeep for example, you might have a strong case by saying something like "The stipend just barely meets the cost of living for this city, but I have X expenses in additional to standard living costs. I am worried about my ability to maintain my health and pay the bills with the current stipend. Are there any other additional sources of funding that I might qualify for? If it helps, I can provide offers from schools B and C (name them) that are providing stipends that would cover the cost of living and my additional expenses."
I think you should be honest and direct with your request because 1) the department will be more likely to respond if they feel that you need this money, not just "want" it, 2) maybe your department doesn't have a fellowship to help cover whatever your extra costs are, but maybe there is some benefit program** that you don't know about yet that will make their offer more attractive and 3) naming the other schools and stating that you have better offers could be the negotiation tool that the department needs to secure funding from another part of the University.
(** For example, my school has an award of up to $5000 from Human Resources to pay for childcare and $1200 per year per dependent to pay for dependent health insurance premiums. This information isn't usually mentioned in the offer letter but if a student has these expenses, it basically increases the value of the offer by up to $6200 per year. If you don't ask, you might end up picking another school that has a higher stipend value on paper but will still cost you more for the other expenses).