My process is to speak individually to each of the protagonists. What I am looking for is whether there is a possibility of change or movement in how they are seeing the situation and, as a result, how they might then react differently to it.
Only if that potential for a shift of perception is in place, do we go ahead and meet. In this way, I can guarantee a good outcome.
If we do not go forward to a joint meeting, I can recommend alternative courses of action.
In these situations, it is important to know that mediation is one of the ways forward, not the only way, with all hopes pinned upon it.