You realize that there are legal scholars already positing their legality right now, right? It's not too hard to search Google to see some of the more interesting papers being written on the subject from the legal point of view.
The social and psychological aspects are still scarce since we live in a society built around western European Protestantism (heteronormative). So, whatever research that does exist is relatively new or limited in scope.
> You realize that there are legal scholars already positing their legality right now, right?
Of course. On my list of social causes worth spending time and energy on, polygamy ranks pretty low. If it's near and dear to your heart I wish you the best of luck.
It's not so dear as you wish to be. I merely recognize the nature of law is not unlike any other logical enterprise. When you allow one form of inference the other forms that depend upon it must be analyzed to see the limits of it. Just like how legal scholars debate the limits of speech even today. It's both academic and practical.
The social and psychological aspects are still scarce since we live in a society built around western European Protestantism (heteronormative). So, whatever research that does exist is relatively new or limited in scope.