Do you know the story of the man who left 17 camels to his three sons upon his death? To his eldest he left half, to the next boy 1/3 and to the youngest son 1/9th. Unfortunately 17 cannot be divided by half, 1/3 nor 1/9 and the sons began to bicker.
Nearly giving up, they brought their plight to the wise woman of the village who said, "I don't have an answer for you, but if you'd like you can have one of my camels."
Now they had 18 camels: the oldest took half or 9, the middle boy took a third or 6, and the youngest took a 9th or 2. What to do with the camel left over? Give it to the wise woman, of course.
Over what resource are you bickering with others? Can you expand the pie, even momentarily, to see if doing so gives everyone enough of what they want?
What is needed to see the possibilities is either 1) an outsider, such as the wise woman or 2) one member of the group to step outside. A wise woman is not always available. We have to be able to step aside from the emotionality of our situation and look around to say, "what are the possibilities? In what way are we seeing this in black and white -- where is the gray? If no gray is obvious, can we create it?"
I was in a class once where the teacher asked, "what is impossible to do today that if it were possible would make a significant positive impact on your achievement of your goals." What is surprising about that is that once one lists the impossibilities and their impact, suddenly ways of gaining even small parts of those previous impossibilities become visible.
Can you step outside your current negotiations or conflicts and see a third way?