Really only Polygyny (one man, multiple women). Any other version has never really worked and in the grand majority of, if not all of those instances of polygyny, the woman is held as somehow fundamentally inferior to the male. So it only makes sense that polygyny may develop. If we are going to treat the woman as "stuff" then it only makes sense to want the most "stuff". Polyandry (the opposite) is only practiced in a couple far east countries where the two men tend to be brothers and the environmental resources are scarce. Group marriage (multiple men AND women... which is essentially what you are proposing) has never worked ever and has only been practiced in places such as hippie communes.
I was trying to do this without using gender bias, but I will claim that this much is true. Men have a greater biological tendency to seek multiple mates than women do. My point, however, was that you claimed that polygamy is doomed to failure, and this is observably false.
You also made another assumption, there: "Polygamy is most commonly practiced in male-dominated societies; therefore, it is the only type of society in which polygamy can flourish." You're begging the question.
biological support maybe, but not psychological. group marriages have NEVER been favoured and polyandry only in very specific circumstances. Polygyny only occurs when women are treated as less than men.
Again, this is false. Open marriages and relationships have a greater mechanism for allowing its members to function sociologically, for reasons I've outlined earlier.
A question that many of my classmates failed to get correct in class was this "So, the cancer cells in all of the rodent studies seemed to react in a positive manner to the treatment, so why didn't the human cancer cells react the same way?" The answer was quite simple to me, and anyone else who didn't overthink the question: Humans aren't rats.
It's easy for us to look at ourselves as "above" other mammals, and even our own baser instincts when we say things like "We're civilized. We're intelligent creatures. We're not animals."
But we ARE animals. Unbelievably intelligent animals, yes, but animals nonetheless. Whether we choose to admit this or not, we DO have baser instincts, and to shut them off would be to LITERALLY kill ourselves. After all, we have an instinct to eat. We have an instinct to find shelter. We have an instinct to gather into a society and support each other. ALL of those things we share with rats, the creatures we're so "different" from. We're not "above" our own sexual nature. We just try to put a shiny, pretty coat on it to mask what it really is - an instinct to get together and copulate, so we can multiply as a species and not go extinct. Anything beyond that is just the icing on the cake.
I'll add in another thought here, too. It's funny you mention that humans aren't rats. Do you know why rats are used in so many biological and medical experiments? Because they're so similar to humans on a biological level. Think about it.
. But c'est le vie no?