Obtaining feedback from supervisors
If by "supervisors" you mean your dissertation committee, then, as far as I know, the standard approach is to allow the committee chair (advisor) to resolve various conflicts of that kind between her/him and committee members.

At many universities (well, at least, at some, mine included), a Ph.D. student is actually prohibited from direct communication with committee members — in particular, on dissertation (manuscript) revisions' feedback — so, this burden is a part of the advisor's responsibilities. Perhaps, such arrangement is not common across universities within a country and across different countries.