In one of the passages that Peter Lombard quotes the Damascene, he is puzzled how John can claim that the Father, Son and Spirit are one God, just as "Peter, John and Paul" are three men and a single human nature. He resolves the contradiction (because even in spite of the fact that he has Abelard's Sic et Non, he still holds the the late Patristic claim that the Fathers cannot contradict one another!) by saying that John means this merely analogically.
Actually he doesn't. But there's no contradiction anyways-let me explain.
John holds the same ontology as the Cappadocians. The Cappadocians held an Ultra-Realist ontology. "Realism" in the medieval sense, is the idea that there are "Real" universals- like "catness" for cats or "humanness" for humans. The alternative view is "Nominalism," which holds that universals are nominal, namely, we see a bunch of stuff that looks similar and then we give it a common name. So, there are only individual cats, but no "catness" apart from our words.
"Ultra Realism" holds that there is a single human substance- just as all universals are in fact single substance (one can see the problem with this view, that is, it might be taken to encourage pantheism). So, "Peter, Paul, and John" are a single entity, because all humanity is a single substance. Every time, claimed Gregory of Nazianzus, a new human being is born, a new accident on that substance comes about.
This makes the Incarnation rather interesting, because, in a sense, when Christ is deified and ascends to the right hand of the Father, so does the rest of the human race. Bear in mind that those who used this ontology the most had Origenist influences (namely, the two Leontiuses and Gregory of Nyssa- hence universalism wasn't a problem for them). At the beginning of Book 4 of De Fide Orthodoxa, John states that it's possible to say that all humans have ascended and all are redeemed, since our very nature sits at the right hand of God already. He then states that we cannot go that far though, because the 5th ecumenical council has rejected and condemned the heresy of Origenism.
Anyways, since "Peter, Paul, and John" are a single entity, even if they are different persons, they are similar to the Trinity. Gregory of Nazianzus (who BTW, is the one who uses this analogy) states that they differ from the Trinity because there is a greater abundance of accidental qualities between them. If one erased these, then they would be a unified into undiscernible difference. Of course the Trinity lacks accidental qualities (having an existence that is not distinct from essence as Aquinas would put it), but it is distinguish by way of differing relations.
Now, this means that (contrary to what a lot of modern theologians claim) that the Cappadocians aren't saying anything different than Augustine. It's just that Augustine has a different ontology and therefore expresses himself differently. He can't use certain analogies like the three men, because in his mind they are really, three entities, something they are not for the Cappadocians. In fact, in De Trinitate he pretty much rejects this analogy as one would expect.
Certain modern theologians (notably, Jenson, Moltmann, Pannenberg) want to say that the Trinity is made up of three different subjects, and that Augustine everyone else in the western tradition turned from the pure doctrine of the Cappadocians and is now pretty much Modalist as a result. But that's not right, because they're interpreting the concept of person as a modern person, and aren't taking into consideration the ultra-realist concept of being. Hence, Jenson, for example, has endorsed Tri-Theism with statements like "God is what happens between Father, Son, and Spirit." This is highly problematic from the perspective of historic Christian orthodoxy and not what the Fathers of the Church taught either.