Wendy - I'm not a co-op lawyer, but I am a commercial litigator with decades of experience and have served on three co-op boards. Mediation is generally conducted by a trained mediator who can professionally evaluate the strengths and weaknesses of each side's position and guide them to a voluntary resolution. Board members would not ordinarily have that expertise. But even if they did, they are likely to be perceived as having conflicts of interest by one side or another. If the dispute involves one or both shareholders violating house rules or the proprietary lease, then the Board's role is to police and enforce the rules. If it is a dispute that does not involve violation of the rules, then the board should stay out of it. But of course, a dispute that disturbs neighbors likely violates the rules.