There were three types of marriage in classical Rome: confarreatio, connubium and contubernium, I think they were called ( I could look it up). the first was upper class, clan power relationships and land and money, so obviously monogamous, though divorce became very common by the time of the Empire. The last was "shacking up', informal, the normal for poor people. So probably sequential or lasting single relationships, like America now.

And of course the rich had access to slave women (etc) just like American plantations.