Immutable, impassible, and entirely self-sufficient, God does not need anything or any other being. Omnipotent, omniscient, omnipresent, and omnibenevolent, God is also not constrained or limited by anything or any other being.
God is so free that his essence and existence are indistinguishable, making him utterly distinct from all other beings, all of which he created from nothing, none of which he needs.
Put another way, God is perfectly free to be God, and there is nothing in the cosmos that does or can interfere with or influence his godly freedom, not even his Creation, which he transcends.
The only limits or constraints God experiences are the ones he sets for himself. More specifically, those that do not contradict his nature—his perfect wisdom and character.
One notable limit God sets himself is the inability to create another god.
Omnigod is also a mono-god. He does not want or need other gods. And even if he did, he couldn’t create any.
As free as God is, he is not free to create other gods.
Try as he might, God could never raise any of his creatures to his level because it is logically impossible for him to do so.
Moreover, God’s “free” actual creatures could never utilize their freedom to become god-like or attain godhood.
Thus, the freedom inherent in God’s created “actual” beings cannot and never will contain any seed of godhood.
Any created freedom that contained even a hint of godhood would not only contradict but also serve as a direct assault against God’s freedom, which is the only uncreated freedom in existence.
Of course, classical theism incorporates all of the above into its assumptions concerning God’s overarching divine purposes for Creation.
I don't know about you, but those assumptions come off as awfully limiting, for both God and man.
All I can say is this -- God's overarching divine purposes become much “freer” and perhaps even more logical when one entertains the simple assumption that all freedom --not just God's--is uncreated.
Note added: I used impassable when I mean impassible. H/T to Bruce Charlton for catching that and bringing it to my attention.