Since the 39 Articles prescribes three ancient creeds for subscription, the Apostles, Nicene, and Athanasian, I think it would be good to examine the text of the Athanasian creed to note some of its more curious features, especially in the light of the classical theism debate.
The Athanasian Creed, for some reason, picks out certain features of divinity to indicate oneness of that specific feature. Here's the passage in question.:
The Father uncreate, the Son uncreate: and the Holy Ghost uncreate.
The Father incomprehensible, the Son incomprehensible: and the Holy Ghost incomprehensible.
The Father eternal, the Son eternal: and the Holy Ghost eternal.
And yet they are not three eternals: but one eternal.
As also there are not three incomprehensibles, nor three uncreated: but one uncreated, and one incomprehensible.
So likewise the Father is Almighty, the Son Almighty: and the Holy Ghost Almighty.
And yet they are not three Almighties: but one Almighty.
So the Father is God, the Son is God: and the Holy Ghost is God.
And yet they are not three Gods: but one God.
So likewise the Father is Lord, the Son Lord: and the Holy Ghost Lord.
And yet not three Lords: but one Lord.
Thus we have one "eternal", one "incomprehensible", one "uncreated", one "God", and finally one "Lord". The question at hand is why did the creed pick out those specific features to explicitly specify oneness, but yet not any other feature of property of divinity. Why doesn't, for example, the creed say, "The Father is loving, the Son is loving, and the Holy Ghost is loving, but there are not three loves but one Love" or "The Father is all knowing, the Son is all knowing, and the Holy Ghost is all knowing, but there are not three all knowings but one all knowing"?
A hypothesis here would be that the creed is trying to emphasise the unity of divinity and "eternal", "uncreated", and "incomprehensible" are, in some manner of speaking, exclusively core to divinity in a way in which knowing or loving is not, they are, for the lack of a better word, the epitome of "transcendentals" properties. Thus, human beings can know, love, etc, etc, but eternality, being incomprehensible, and uncreated are categorically excluded from humanity or creaturely stuff. Thus, to constitute one divine, it is sufficient that they be one in eternality, uncreatedness, and incomprehensibility. To use their language, those are properly part of the one "divine substance".
As such, if this hypothesis is correct, then what is significant would be the properties it does not single out for saying that there is only one. As such, we can speak of there being three wisdoms, three omniscients, three omnibenevolence, etc. The text of the Athanasian creed would itself be compatible with social trinitarianism or each person of the trinity having its own will because it does not identify what properties properly belong to the divine substance as opposed to the persons, save for the three features above.
Second, I would like to look at this rather curious phrase concerning the unity of Christ's humanity and divinity:
For the right Faith is that we believe and confess: that our Lord Jesus Christ, the Son of God, is God and Man;
God, of the Substance of the Father, begotten before the worlds: and Man, of the Substance of his Mother, born in the world;
Perfect God, and Perfect Man: of a reasonable soul and human flesh subsisting;
Equal to the Father, as touching his Godhead: and inferior to the Father, as touching his Manhood.
Who although he be God and Man: yet he is not two, but one Christ;
One, not by conversion of the Godhead into flesh: but by taking of the Manhood into God;
One altogether, not by confusion of Substance: but by unity of Person.
For as the reasonable soul and flesh is one man: so God and Man is one Christ.
I wish in particular to focus on this last line: "For as the reasonable soul and flesh is one man: so God and Man is one Christ." This appears to be the literary form of a simile, "For as the heaven is high above the earth, so great is his mercy toward them that fear him." (Psalm 103:11)
Yet how far can we take this simile? If there is to be a strict comparison between how the soul is related to the body of a man to how the divine Word is related to Christ's humanity, it would suggest a sort of demi or neo-apollinarianism. The soul after all is where the person's will is located, it is what controls the body even if a person's experience could be "distributed" throughout the body, does the divine Word occupy the human body in exactly the same way the soul occupies the body, the divine Word or Son of God being the will of the human body and controlling the body/humanity in exactly the same way the soul controls the body?
I think that would be an interesting question to explore, however, it does seem that the use of this simile would render a demi-semi-neo-apollinarianism an acceptable option.
Ultimately however, being Anglican means that curiously, as far as christology is concerned, one need only subscribe to the Athanasian creed and not the Chaledonian definition and any other post Nicene Christologies.
And as the 39 Articles state, the three creeds "ought thoroughly to be received and believed: for they may be proved by most certain warrants of holy Scripture", not because the Fathers were wise or whatever, thus the Bible supplies the context and premises for the creedal terms and not the Church Fathers.