When searching the internet on the subject of escalation processes, one sooner or later will encounter the nine escalation stages of Friedrich Glasl. These describe how two parties may first find each other in a position where interests become fixed positions and, after having gone through several stages of increased anguish, finally find themselves at the brink of the "nuclear option", in which they rather destroy the "enemy" without regard for their own future, than behave save everyone from disaster.
In my view it is not necessary to solely view escalation as an emotional process. Although one cannot deny that, often, a certain level of disagreement may have emotional side effects, there is nothing against not being able to agree.
The important thing is to be able to admit that on that given level in a project a solution cannot be reached and to be prepared to escalate the solution to a level where that issue can be solved.
Therefore, in any project it is important to establish a mechanism which incentivises the people involved to solve an issue as soon as possible on their own level of authority. If such solution cannot be reached within a given timeframe, the mechanism should allow them to escalate the issue to a level where it can be solved, for instance because of a higher mandate or of "higher" technical, contractual or financial expertise. People engaged in complex projects should not waste their energy on trying to solve issues they are not capable of solving. That usually leads to frustration and emotions. Projects should be fun (at least parties should try to establish such culture). And problems should be solved at the level where these can be resolved.