Try…their point of view. Both should rather try to find a solution. How did they arrive at their current position. Why they might be under pressure to hold their position. Let me see if I can summarise your position: you want X because of Y. Clarify until they agree with your summary.
Invent…win-win. A win win agreement. Each side wants different things. Find a way so both can get the thing they want. What differences can be leveraged?
Insist…using objective criteria. Act like a judge. Insist on using objective criteria to solve the case. Ask: what is your basis? Or. How did you arrive at that? Ask yourself: how would a court decide this? Research: professional standards, existing precedent, cultural norms, fair market value, potential arbitrators.