Brainstorm the assumptions driving each person's position or needs. The other person should ask and record. Do not challenge assumptions during the brainstorming process. Just write them down.
Each person can offer up any assumptions he/she thinks the other person may hold. These can only be added if the other person agrees.
If there are facts or data to challenge an assumption, discuss the facts or data and the person's assumption. The sticky note can only be changed if the person agrees.
Check the assumptions to see if there are any themes. If there are, record these on sticky notes.
Test if there is a possible win/win solution.
Do a process and content check: Is the conflict defined properly or is there something else that is really in conflict and the statement of conflict is just a symptom of something else that is going on. Revise the statement of conflict if necessary. Have all the key assumptions surfaced? Does each person feel listened to? Validated?