supernumerary vs supererogatory

supernumerary is a noun but supererogatory is not a noun.

Word	Noun	Adjective	Verb	Adverb
supernumerary	Yes	Yes	No	No
supererogatory	No	Yes	No	No

As adjectives, supernumerary and supererogatory are synonyms defined as:

supernumerary and supererogatory: more than is needed, desired, or required

Other synonyms of supernumerary include excess, extra, redundant, spare, superfluous, surplus.

supernumerary (noun)	supererogatory (noun)
a minor actor in crowd scenes
a person serving no apparent function

supernumerary (adjective)	supererogatory (adjective)
more than is needed, desired, or required	more than is needed, desired, or required