The Essence of the Trinity is Nothing Else Than the Trinity Itself

… the essence (of the Trinity) is nothing else than the Trinity itself. (St Augustine)

It is common for the Western tradition to be accused of a kind of modalism because of discussions about the substance of God, and these discussions preceding discussion of the Trinity. It doesn't seem that way to me, although it is true that the idea that there is a being of God behind Father, Son and Spirit is very much alive and well in the western church. (A sort of fourth behind the three.) I suspect that this is how many people understand the Trinity, and reject or accept it on this basis. St Augustine is often cited as an example of this error. But not so. Augustine thinks that the substance of the Trinity is the Trinity itself. The divinity of Father, Son and Spirit is held in common and is not a sort of fourth person or 'stuff' behind the three. This is perhaps one reason why St Augustine is loathe to answer the question, 'What are these three?" He wishes us to avoid thinking of some kind of 'stuff' of which Father, Son and Spirit are three examples.

The Father, the Son and the Holy Spirit are the Trinity, but they are only one God; not that the divinity, which they have in common, is a sort of fourth person, but that the Godhead is ineffably and inseparably a Trinity. (St Augustine)

There is no divine substance apart from the relations of the three. The Father, the Son and the Spirit are the Trinity, and there is nothing missing from their co-equal divinity and nothing 'ontologically' behind them. Without the personal identities in the relations of the three there is no God, no divinity, nothing, literally. This means that, if we include some characteristic within the eternal relations of Father, Son and Spirit, we cannot avoid this characteristic's inclusion into the very being of God. If we do posit a characteristic of the eternal relationship between say, Father and Son, like subordination, and we wish to avoid subordinating the Father and Son in their being (that is, ontologically), then we must separate the being of God from the relations of the three. And that is heresy.