Similarly, the unity cannot be nailed down by an Aristotelian secondary substance (deutero ousia) or essence. Let me explain. Someone might think to interpret the identity claim
The Father is God
in which the the 'is' expresses identity, as a predication, to wit
The Father is divine
where the 'is' expresses predication and not identity. One could then say that the secondary substance divinity, which is exemplified by the F, S, and HS, is what secures their identity. In this sense, the three persons could be said to be consubstantial. But how could the unity of God be the unity of a secondary substance? This suggestion won't work because it allows there to be three gods. For if you say that the F is divine or a god, and the S is divine or a god, and the HS is divine or a god, then you are committed to tritheism.
To block this outcome and secure the divine unity, one must interpret 'The Father is God' as what it appears to be, namely, an identity statement. But then the distinctness of persons goes by the board.
I am not convinced. Whether or not this option allows there to be three gods is entirely a question of what it is to be God, not a general fact about secondary substances. If I say, "This is an apple, and that is an apple, and this third thing is an apple," I have indicated three apples. But this is due to the nature of apples, not due to their having the same essence or nature or secondary substance in common. To say, then, "The Father is God, the Son is God, the Holy Spirit is God" can only indicate three Gods if it is in the nature of God to be divisible among distinct particular Gods having that nature (in the way the nature of apples is divisible among distinct particular apples having that nature). And it is not; that is the point of the doctrine of divine simplicity. Thus there is no reason to think that this view implies that there are three Gods.
This interpretation also has an impeccable pedigree, historically speaking; it is Cappadocian, e.g., you can find something like it in Gregory of Nyssa's To Ablabius on Not Three Gods, and something like it is found in Aquinas. (Indeed, it is hard to find anyone who takes an identity view in the whole history of orthodoxy. In some translations Aquinas sometimes sounds like it; but medieval 'idem' and 'identitas' often indicates 'agreeing in species or kind or predicate or property' rather than identity in our sense; and Aquinas simply seems to be saying in technical terms that the persons, while distinguished from each other by real distinction, each share exactly the same nature - which would be the above interpretation.)
The Quicunque vult says:
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.
And on the above view, this is entirely coherent; the first sentence, taken as expressing predication rather than identity, does not imply three Gods if the divine nature is not divisible in the way that (for instance) the nature of apples is. And since there is no reason to think it is, and much reason to think it is not, the above two sentences are entirely consistent. The fact that we are talking about a nature or essence does not, in itself, imply anything about how the nature or essence is divided among its subjects; at least, I have never seen a good argument that it does (one, at least, that is more robust than "Most natures we know are like that," which is not a strong basis for making any claim about the Trinity).
