All of God does all that God does. But then it’s only the Son who is incarnated. Both are standard affirmations of classic orthodoxy, and it’s a trick to keep them together.
In a brief summary of Augustine’s trinitarian thought in The Quest for the Trinity: The Doctrine of God in Scripture, History and Modernity, Stephen Holmes points to Augustine’s solution in his exegesis of John 5:19 (the Son does what He sees the Father doing). It’s nifty:
“Augustine’s own interpretation aligns the Father’s showing . . . and the Son’s seeing with the eternal relation of origin: ‘the Father’s showing begets the Son’s seeing in the same way as the Father begets the Son.’ Given, however, Augustine’s constant commitment to simplicity . . . the Father is necessarily identical with his act of showing, and the Son simply identical with his act of seeing. This movement of showing and seeing, then, is identical with the Father’s begetting of the Son.”
The payoff is that there is an order within the necessary and, for Augustine, the single act of the Father and Son; the Father shows and that begets the Son’s seeing. But the order is an order of reciprocity: “the Father’s showing requires the Son’s seeing just as being the Father requires the begin of the Son. In the text from John’s gospel, this showing and seeing is referring to divine works; Augustine has thus argued for an inseparability of divine works, but also for a proper ordering of the persons in the inseparable work, both of which are based in the eternal relations of origin within the Trinity” (133-4).
Because of the sort of action it is, the Father’s act of showing is no act at all unless the Son acts in seeing. It’s not the kind of act that a single person can perform on his own. Yet, Augustine does not say that the “showing” is the united act of Father and Son, as is the “seeing.” That would erase the give-and-take within the single action. So there’s a single, united action, but internally reciprocal and differentiated, so that it demands the united act of Father and Son, and, implicitly, the Spirit, who is the light of the Father’s showing and the Son’s seeing.
It’s only on such an account that we can actually affirm the united action of the Persons at all. If “showing” and “seeing” were each acts of all the Persons together, it wouldn’t be at all clear why all of God does all that God does. Why does it take Father, Son, and Spirit to “show”? It doesn’t. But it does take Father, Son, and Spirit to perform the one act of “showing-seeing,” just as it takes Father, Son, and Spirit to perform the single act of “beget-begotten.”
This interpretation fits beautifully with the Cappadocian claim that every opera ad extra originates from the Father through the Son and is completed in the Spirit, for of Him, through Him, and to Him are all things. There is one divine operation, but differentiated as of, through, and to.