Interesting point. By polygamy, I assume you mean one man with multiple wives. I have a better suggestion based on some of my reading: Group marriages. A family may have a marriage that consists of, say, multiple husbands and multiple wives in the same family unit. All members wouldn't even need to be heterosexual.
It might sound crazy, but the theory is discussed in several of Robert Heinlein's books: Stranger In A Strange Land approaches it carefully, The Moon Is A Harsh Mistress goes into more depth, and, while not part of the original Methuselah's Children story arc, by the time he gets to Time Enough For Love, it is commonplace. He also discusses it in Friday, including the removal of a spouse from the family unit.
It makes more sense than one man with a dozen wives. While that may give a man some variety, his spouses are not much more than chattel. Income is put to the common good of the family, household needs are split among the group, kids never have to deal with being an only child. Cheating on a spouse? If you find someone interesting, discuss it with partners to see if they are interested in a new wife/husband to the team.
As for businesses that refuse to provide services to a legal wedding, I put forth a comment made to me when I was doing Stand Up. I was booked into a traditionally black night club. They didn't worry about your skin color, though. If you walked through the door and had the cash to buy a drink, you were served. Why? Because in business, the important thing is not the color of your skin, but the color of your money.