This is a really high concept question. In other words, I’m not saying “what if the Romans were polygamists?” or “what if the Arabs founded a republic?” Just a very general question of how a classical republic where polygamy is common (at least among the elites) might look. Off the top of my head, I can’t think of any particular societies that fit this description.
Consider how inheritance and political dynasties might work in such a society. How about political marriage alliances and the like. Is it more likely that such a republic would be more equal or less equal?