In some styles of mediation, particularly community mediation, it is usual for the mediator to meet the parties before the actual mediation. Some commercial mediators also have pre-mediation meetings. This does add some cost, but the results can be very positive.
I had a case where the parties felt it would be helpful for me to visit the premises concerned, which I did a few days before the mediation, with representatives of all three parties. This not only helped me, and the other parties who had not seen the premises, to visualise the nature of the problems and issues, but more importantly, gave the occupiers an opportunity to say what they felt needed saying to the representatives of the other parties.
There was a great deal of emotion, and by allowing this to come out before the actual mediation, I am sure we were able to make progress more quickly on the day. A settlement was reached by early evening. The pre-visit will have saved time and cost on the day.
While such a meeting is not appropriate in many cases, it is worth considering as a possibility. It may even save money.