The question, I believe, is what legal recognition can you get for a second or third, fourth concurrent spouse? None of our systems are designed for that. There’s immigration rights - if your spouse(s) are not citizens. Only one marriage (presumably the first) is recognized by most western governments. (You could, like one Afghani immigrant recently on trial near Ottawa for killing one wife, claim the other one is your “sister” and her family.)
For pensions, for legal divorce proceedings, tax filing, etc - only one wife counts, and you probably can’t play muscial chairs (? or whatever…) to pick the one who is advantageous in this situation. One spouse becomes the “official” one.
In the situation mentioned above, One wonders whether when the first wife “divorced” so the second wife could be immigrated, whether the existing marriage then became recognized or whether the fellow had to remarry the next spouse in line for immigration, after the first one’s divorce went through. That detail -date of marriage - might indicate the legal validity the Immigration people put on locally valid polygamous marriages.
In all the birther moronicity before the last election, there was the interesting tidbit about whether Obama’s father had in fact divorced his first wife back in Kenya, before marrying Obama’s mother. Apparently the details on this are not clear. IIRC the immigration department interviewed him and he stated that he had indeed divorced, but I suppose paperwork is sparse. Regardless, they took no action lacking any definite proof.
So the only question is whether where spare spouses are given any special legal recognition, and generally the answer seems to be no. Whether the head nurse will consider you “gfamily” and let you visit in the hospital is likely an individual decision. What’s really interesting is how wills handle this (or better yet, intestate). In the strict legal sense, the one person recognized as spouse by the system probably has all the claim.
A good question to ask would be whether there are any special considerations with the mormon splinter groups and such - since in North America and some western countries, many jurisdictions give (almost) equal weight to common law or cohabitation arrangements.
An interesting side note - I have been told that for Canada Pension Plan (the rough equivalent of Social Security) the rule is the person cohabitating with the deceased for at least 6 months gets the survivor pension, even if there is a surviving legal spouse. This gets around the situation of a person who separates, never divorces, moves in with someone else, and years later they die and the wife they haven’t spoken to for 10 years gets the money. No indication what the rules are for multiples, but the rules are written for a single spouse. I suppose, based on the news about polygamous societies in British Columbia, that the other, underage spouses might qualify for a dependent’s survivor pension until 18?