Are there intractable legal problems with polygamy?

Over in this thread, we are discussing whether the same arguments in support of SSM can be applied to polygamous marriages. The question of how easy it would be to actually implement polygamy within the construct of current laws was brought up, with some saying that it would be very difficult to deal with things like inheritance, benefits, divorce, etc.

I claim that none of these problems are actually that hard to solve at all, and in fact have already been solved in analogous cases in many ways. In the OP, I will mention the proposed problems I have heard, and offer my solution. I’m interested in discussing other possible problems or whether my solutions are good ones. Most of my arguments are short, but I will be happy to expand on them if there is ambiguity. I want to get this thread started before the above linked one gets too side-tracked.

Problem: Power of attorney. What do you do when the spouses do not agree on the course of action for an incapacitated spouse?

I claim that this has already been solved for the case of a parent with multiple children who do not agree.

Problem: Benefits. How do you give benefits out to families that could have arbitrary numbers of spouses

Again, already solved in the case of families with arbitrary numbers of children.

Problem: Custody. Who gets the children if families split up.

As far as I understand, custody hearings are usually based on a variety of factors, including who the biological parents are, who can provide the best home for the child, and the individual child’s preferences. These would work just as well in polygamous marriages. Arguably, this is a very difficult decision to make, but I don’t know that it’s any more difficult than the monogamous case.

Problem: Divorce/Remarriage. What happens if A,B, and C are married, but then C goes off to marry D? What happens if A and B want to divorce from C and D? What happens if A wants to stay married to B and divorce C, but B and C want all three together?

All of these problems are complicated, but I think that all can be solved if we agree on a particular implementation for polygamy, or at least if all of those involved agree on a particular implementation. A marriage can either be N people who wish to form a union, or it can be M separate 2-person unions. Once the framework is decided on, there are logical solutions to the above problems. In case 1, either the CD marriage is null (because C is already married), or it is a legal union (but one that A and B aren’t necessarily involved in), respectively. Similarly for the others.

These questions have all been addressed in previous threads on polygamy in GD. In general, IIRC, the consensus has been that the practice, assuming consensual adults and specific marriage contracts, is unwieldy but possible.

Why is polygamy considered to be so bad?
Would polygamy in a society that had equality between the sexes be a better deal for the women involved, or for the man?
Polygamy - non-religious objections?
Why is polygamy immoral?
Gay marriage, then polyamory, please.
Next Step in the Debate: Polyamorous, multiple-partner marriages?
What’s wrong with polygamy?
Should Polygamy Be Illegal?