supernorma

supernormal \soo-per-NAWR-muhl\, adjective:

1. In excess of the normal or average: supernormal faculties; supernormal production.
2. Lying beyond normal or natural powers of comprehension: supernormal intimations.

On the other hand, the voyager may also feel that he possesses supernormal powers of perception and movement, that he can perform miracles, extraordinary feats of bodily control, etc …
-- Timothy Leary, Ralph Metzner, Richard Alpert, The Psychedelic Experience

The limbs twitched, the eyes gleamed, the blood-pressure appeared heightened, and there was a supernormal pinkness in the epidermis of the cheek.
-- P. G. Wodehouse, Summer Lightning

Supernormal was first used in the 1860s. The prefix super- has a number of common senses. In this case, it is used in the sense of "an individual, thing, or property that exceeds customary norms or levels" as in superstar.