We recognize two senses of “father”: in one, Solomon might well have been a father (1) to over a thousand children, in another sense he never could have been a father (2) to that many. Fathering (2) requires personal intimacy and so isn’t scalable to a thousand members. Now if political relations are not scalable, they to allow for the possibility of a politics (1) that isn’t politics (2).
The common good of a family involves more than just fathering (1), since otherwise even orphans would be in families, and for the same reason, the political common good requires politics (2). At some point of expansion, we will find a higher polity (1) that isn’t a higher common good. And so while there is some common good above the family, it doesn’t follow that it is the nation or the “International community”. Perhaps neither of these is a political common good.
It’s unlikely that one could set a strict number of persons beyond which we can have only politics (1) and not politics (2). But one thing that’s been suggested throughout this series is that the Left-Right division of ideologies marks a point where one has only politics (1).