TR Superman is multiversal+ but not omni, at least in-comic. The fact that there was even a battle between them is proof of that. But it is true that Superman's story is so powerful that even Mandrakk, who eats plot, had no power over it. I don't even think DC has power over it. The idea of a person who exceeds the realm of imagination, who exudes possibility and hope, physically and mentally stronger than anyone, bound to protect the people of his planet... that idea will always exist as long as man exists.
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