Socities have a Unity of Order, constrasted with the Unity of Substance, a useful example is a human person, and mere aggregation, people in a line, say.
This Unity of Order is a real Unity. At the end of the six days of creation, creation is crowned not with a new natural kind, or an aggregation of parts but the first society, the marriage of Adam and Eve.
This proper ordering of Adam and Eve in society, in specifically marriage, is the last act God performs before declaring creation “very good.” What made creation very good, is not yet another kind, but the proper ordering of creation. The typology of Adam and Eve’s proper ordering in marriage is of keen interest to both Jewish and Catholic exegesis. It is considered a type of Israel and the Church, respectively.
Indeed Augustine tells us that “Creation is for the sake of the church.”
Sweet Talk 
After the kingship descended from heaven, the kingship was in Eridug.
Cities are dragons: they collect treasure, they fight knights, and they can eat you. The first civilization came down into the first city — and the first city was the first of a new type of system, a type which civilization cannot do without.
A city is just a collection of people and resources, but it’s still a dragon; a family is just a collection of people and resources, but it’s still a unity; a computer is just a collection of sand and plastic, but it’s still a computer.
It’s probably possible to circumvent the analytic/bottom-up vs. Hegelian/top-down debate by recognizing these unities of order. (A possibly-equivalent piece of jargon that would be more likely to be recognized is ’emergence’, but that doesn’t come with the shock value of actually paying attention to over a thousand years of accumulated wisdom.)
Notes:
1) It is probably possible to circumvent the analytic vs Hegelian dialietic as you say. Catholic Social Doctrine rose from scholastic philosophy in contradiction to the political novelities of Socialism and Liberalism. It occupies a philosophic place prior to and in reaction against, the modern dialetic.
2) A Unity of Order is a real agent, a group person distinct by reason of dignity. “Just a collection of people” therefore is not true. A line is a collection of people, but a line is not a society, and therefore not a group person. A business deal has intersubjectivity but does not aim at unity as an intrinsic good, and therefore is not a society but a mere partnership. Wherever there are plural rational agents aiming at common ends and where their unity is one of the ends being aimed at we have a society, a person distinct in dignity.