How to negotiate with referees of your paper
You perhaps know that journals often have this policy that you either should implement all the changes suggested by referees or withdraw the paper.


Which journals have such a policy?  I don't think this is the case for any AMS, MAA, or SIAM journal, for example, and I'm not aware of any journal with such a policy (although of course I have direct experience with only a small fraction of the journals in mathematics).  Here's how it works in the cases I'm familiar with:

Any changes suggested by the referees are merely suggestions, which do not need to be followed if the author and editor are in agreement.  If the change involves fixing a mistake or correctly attributing work, then no responsible editor will accept the paper until the situation is resolved (either by making the change or establishing that it is not needed).  Matters of clarity are also taken seriously.  However, some referee suggestions are just opinions that the author may reasonably disagree with.

It's perfectly reasonable to write to the editor and say "Here's a new draft of my paper.  I've made changes A, B, and C proposed by the referees, and I'm grateful to them for identifying these issues, but I have not implemented D and E.  I think those changes are not truly needed, because ..."


  what is the best strategy to negotiate with referees?


I'd think of it instead as negotiating/discussing with the editor.  The editor is the one who makes the decision, with the referees providing advice and expert opinions.  Ideally, you'll be able to convince the referees that not all of their proposed changes are necessary, but the editor is the only person you need to convince if the referees are stubborn.

Editors are used to this.  As an editor, I've occasionally written an acceptance letter (conditional on revisions) that says explicitly that only some of the changes are really needed, and even when I don't say so authors certainly don't always make all the changes.