"It is impossible that God should produce a being like Himself" - Maimonides, Guide for the Perplexed, Part III Chapter XVWhen we talk about the question, "Is there anything that God cannot do?", sooner or later we come to the question: Are there things that are genuinely, absolutely impossible? For example, a thing cannot be both a triangle and a square; that is self-contradictory, and so it is impossible. If something is impossible, then even God cannot do it, and it is not considered any kind of shortcoming or limit to God. Instead, it is considered a property of reality: a thing is itself, and not something else.
Maimonides says it's "impossible" for God to produce a being like Himself. This is based on his assumptions about what it means to be God. But would a Christian share those assumptions? We'll leave aside, for the moment, any specific question of the identity of any other being or beings that might (or might not) be like God, and instead consider the hypothetical question: If it were possible, what it would mean?
So: Can God "produce" a being like Himself? God Himself has not been produced, so the very fact that the other being is "produced" would mean that this other being is, in some ways, not exactly like God. And the differences do not end there, differences that come simply from the fact of being produced rather than self-existing. In philosophy, God is sometimes spoken of as a Necessary Being, or as the Necessary Being. But for any being that God produced, that being would probably not be Necessary in the same way.
But imagine if God did produce a being like Himself in other respects. If God produced another being like God -- inasmuch as another can be like, while being produced, and not in the same way Necessary -- what would it mean for the concept of God, and what it means to be God? If He is no longer entirely alone, if He is now capable of fellowship and relationship -- then God has expanded what it means to be God. Has he altered the equation of the universe? Are fellowship and companionship now part of what it means to exist? Has he changed the foundation, whether the idea of Necessity has such a key place in our world and in our understanding of it, since he has done something so foundational that is so clearly not Necessary?
If God were to produce another being like Himself, and if the point is fellowship and love -- if the point is that it is not impossible to be like Him -- then that may alter what it means to exist in our universe, to be a part of our universe. It may also alter what it means to understand our universe.