Does The First Way Give Us Uniqueness?

My philosophy of religion professor posed this challenge to me. Professor says the arguments for God's existence don't prove uniqueness (that is, these arguments do not prove one single God is responsible), including Aquinas. I said, appealing to Aquinas First Way, that there can't be more than one thing that is Pure Act because if there were, there would be some potential to distinguish between them. Professor replied that assumes the indiscernibility of identicals, which is by no means obvious. Consider a sphere with equidistant points on the surface. They have no distinguishing features to differentiate between one and the other, yet they are not all the same. 

The tempting answer is to appeal to space and relation, but it seems every space point has the same relation. My friend Christopher shared with me his thoughts and I thought they were worth sharing here so that I can reference it in the future. 

You don't have to argue from the identity of indiscernibles. Simplicity/pure actuality gets you identity between God and Esse Subsistens. And there can only be one existence. Why can there be only one existence? Because it's a universal participated by anything that is. So if there were two, they'd both participate in each other and therefore be prior to each other, which is absurd.

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