No. The person of God is embodied in the Holy Spirit. The Holy Spirit does not undergo changes in foundation, or principle. The Holy spirit is alive and handles things as they occur. The incarnation was an event
The concept of the Trinty and trinity in general is contained in scripture. The Fathers didn't have a large set of knowledge to know and understand trinity, personhood, the nature of the world, and what it means "to procede". They were presented with the apparent contradiction of Jesus claiming to be God and the fact that there is only one God. They gave their best explaination which is lacking and nebulous. I didn't contradict it. God is God and man is made in the image and likeness of God.
" Any predictions when this will end? I would think an infinite number of persons could be added to the Divine Nature, right?"
The Jews asked the same question. They identify the Holy Spirit as the person of God.
" BTW, God does not change anymore than Triangles change and add another side and yet still remain Triangles."
The analogy is NG. If you have something specific to address from what I said, go right ahead.
The analogy is spot on. That is the reason you reject it.