“Strong Thomism” is the view that entails Divine Simplicity (DS). DS is the view that God is absolutely simple, in that there are no parts of God. While that sounds good, DS entails the further thesis that God does not have properties. That is to say, the strongest versions of DS state that, literally, we cannot know anything about God. We can only know about what he is not (this is called the via negativa) and can only speak about God in analogical terms. I am not an adherent of this view. In fact, it seems to me that if DS (and hence Strong Thomism) is true, then the Trinity is false.
For Thomas Aquinas (for whom Thomism is named), the Trinity is characterized by relations among the persons. The knower is the Father, the one known is the Son, and the one who is knowing generates the one who is known. The Spirit proceeds forth from these two other persons. This, however, seems to conflict with DS. This is because these relations, if ontologically real, would get rid of DS. There are no real relations in God, on DS, and so no really distinct persons. What would appear to be true of God in a positive sense, namely, God is one being in three persons, has to be literally false. The property being triune is not predicated of him. Instead, these persons more or less become the “names” of God, and we have some kind of unitarianism. The fact remains that on Strong Thomism and DS, the ontological Trinity is literally untrue; God is not a Trinity.
The second objection comes from J.P. Moreland. The idea is that the relations that make up the Trinity of knowing and loving can lead into an infinite regress of Trinities. Each person would have the same distinction of knowing and loving relations in their mind and constitute another Trinity. This would mean that we’d have not only nine persons, but an infinite number, since each of these “new” persons would have Trinities of their own. A further problem is that on this view, persons exist “in” other persons. As far as I can tell, persons don’t exist in other persons. It is for these and other reasons that I do not accept DS in this way.