Even in polygamous societies, men have done many stupid things to keep their beloveds from the inferior position resulting from their birth or captivity, and if the laws got in the way -- why, you could get around them. Or trample them underfoot. One reason why the Inca fell was that they had just been through a civil war, because the last Inca had tried to divide the kingdom between his proper heir, his sister-wife's son, and the son a beloved concubine had borne.
And for good reason. The intrigues of harems are notorious for the obvious reason that they were plentiful. To be sure, it helped that the real female position of power was the Queen Mother, not the queen consort, but sheer jealousy accounted for a lot. Relations between the concubine and the actual wife would be rather pointed. This would go double, of course, if the wife did not have a child, or only had daughters.
Not to mention that even in monogamous countries, the status of mistress was available. Which might or might not have a status like that of a concubine. For one thing, the man could probably make legal arrangements for her, even if he didn't go to the lengths of Louis XIV, who had his mistress's children legitimated. So there is no society of which you could say that it had to be a problem for all characters. The conflict arises not only from social arrangements but from the character of the characters, and their characters can be tweaked to fit into a number of arrangement -- a large number.