I would like to describe something that is even rarer than extraordinary. Does superordinary fit the bill?

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    what about singular? Nothing can be rarer than only 1 something being in existence. Doesn't really clear up your super vs. extra dilemma but the only thing more rare than singular would be nonexistent. – PhotoScientist Jun 29 '18 at 21:10

Despite what you might assume from the individual words, the definitions of extraordinary and superordinary are actually the opposite of ordinary.

Something extraordinary goes "beyond what is usual, regular, or customary," or is "exceptional to a very marked extent."

Something that is superordinary is "superior to or in excess of the ordinary."

But to make up a one-off word using super-something (scroll down to the prefix entry) would be to say that it was "very something." While extra-something (scroll down to the prefix entry again) would mean "beyond something" (which is just another way of saying "very").

Nevertheless, as established single words, superordinary does not mean "even rarer" than extraordinary.

Instead, try unparalleled:

having no parallel; especially : having no equal or match : unique in kind or quality

War crimes of this type are unparalleled in history.
The new telescope offers an unparalleled opportunity to conduct research.
Her knowledge of the subject is unparalleled.

So, you could say:

His abilities were not just extraordinary; they were unparalleled.

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