Supererogate is a word that is seldom used in everyday language, and it can be difficult to find synonyms for it. However, some possible alternatives include exceed, surpass, outdo, excel, go above and beyond, and take things to the next level. These options all convey the idea of doing more than what is expected or required, which is the central meaning of supererogate. Other potential synonyms include over-perform, outshine, and over-accomplish. While these words may not be as precise as supererogate, they can still be useful in conveying similar ideas or emotions.