The UUA's website says, “Because of our strong respect for each person's beliefs and values, each wedding is custom-crafted with a couple to reflect their personalities and relationship.”
I have some genuine questions about this: Would a church conduct a group marriage for polyamorous members? If a man sincerely wanted to be married to more than one wife (polygamy), or if a woman wanted to marry another husband (polyandry), would this be viewed as something that could be done religiously, not legally, speaking. A person may legally be married to one other person, but they may feel like they are spiritually married to others. Have you ever attended a ceremony like this?