In On “Not Three Gods”, Gregory mentions that the persons of the Godhead are united by their operations (works). This manner of speaking has been accosted for the purpose of social formulations of the Trinity, but a careful reading of the way in which Gregory employs the divine operations should dissuade us of any such notion within his own writings. It is not that the Father works, the Son works, and the Spirit works, and their works happen to match up, as if they were synchronized swimmers, but rather the work of the Father is the work of the Son and the Spirit. It is the same work. The work itself moves from Father, to Son, and to Spirit. Gregory explains:
Since, then, the character of the superintending and beholding power is one, in Father, Son, and Holy Spirit, as has been said in our previous argument, issuing from the Father as from a spring, brought into operation by the Son, and perfecting its grace by the power of the Spirit, and since no operation is separated in respect of the Persons, being fulfilled by each individually apart from that which is joined with Him in our contemplation, but all providence, care, and superintendence of all, alike of things in the sensible creation and of those of supramundane nature, and that power which preserves the things which are, and corrects those which are amiss, and instructs those which are ordered aright, is one, and not three, being, indeed, directed by the Holy Trinity, yet not severed by a threefold division according to the number of the Persons contemplated in the Faith, so that each of the acts, contemplated by itself should be the work of the Father alone, or of the Son peculiarly, or of the Holy Spirit separately, but while, as the Apostle says, the one and the selfsame Spirit divides His good gifts to every man severally, the motion of good proceeding from the Spirit is not without beginning; — we find that the power which we conceive as preceding in this motion, which is the Only-begotten God, is the maker of all things; without Him no existent thing attains to the beginning of its being: and again, this same source of good issues from the will of the Father.
If, then, every good thing and every good name, depending on that power and purpose, which is without beginning, is brought to perfection in the power of the Spirit through the Only-begotten God, without mark of time or distinction (since there is no delay, existent or conceived, in the motion of the Divine will from the Father, through the Son, to the Spirit): and if Godhead also is one of the good names and concepts, it would not be proper to divide the name into a plurality, since the unity existing in the action prevents plural enumeration.
~ On “Not Three Gods” pg. 334-335 NPNF vol. 5
Notice that the character of God’s power is one. His will is one. It moves through the persons, yet is one. There is no distinction in it, because of Gregory’s commitment to simplicity and infinity, and so it can move “through” the divine persons without ever leaving them.