Let’s say you’ve reached a stopping or crisis point with someone or some group. No one can see a good way to go forward which will satisfy the parties. There are some points which each side wants honored.
You might actively involve the parties again by getting them to allow this uncertainty and tension just long enough to consider what else is important to them. Perhaps they can generate some ideas about what is important to them in addition to the issues already under discussion.
If they can think of other things which are important to them, it may trigger ideas about how they can each relate to this new variety. Perhaps if some new element is honored, it might change the importance or relationship of some other element which had hampered the discussions. Or, there might be a way to give one party something they want independent of any effect on the other party (connect independently).