No, not likely. I'm no green-eyed monster, but I'm probably just jealous enough to preclude it. But hey... Maybe if I were in a situation where it made sense. Oh, and dear god, look at the way divorce laws discriminate against men at present... Imagine your a guy married with two women - And they then want to divorce you. (!!!). Children or no. You'll be left with nothing (and not the proverbial nothing - real nothing - less than nothing maybe even)
As far as the law is concerned, I think it would be wise that the law insists that marriages should, at least officially, be a closed loop (what's going to change casual human nature after all things said and done). No loose ends.
As in. Anybody marrying a married person, must at the same time marry the other person(s), and vice versa. I think the law should try and prevent situations where somebody is in a marriage, and suddenly their partner wants to marry somebody else in, who they do not want to be in a marriage with. And multiple marriages should not intersect on a subset of the people involved in those marriages.
It should not be one person in an existing marriage marrying somebody else. It should be the people in the marriage marrying another person. Subtle difference. Everybody should willingly, and intentionally as well as legally, be married to everybody else in a marriage. That covers the interest of the consenting adults.
What now about the rights of the children. Will the children legally be the children of all the adults? Will members, in the event of a divorce, have the right to sue for guardianship of children which are not their biological children?
It really could be a can of worms. On the other hand. It could be hugely beneficial for the children if such a marriage persists.
You can bet it would probably be solid gold for Hollywood's tabloid news industry.