There are several synonyms for the phrase "not do." Some alternative phrases include "avoid doing," "refrain from," "abstain from," "cease to," and "stop doing." These alternatives can be useful when trying to add variety to your writing or communication, or when trying to avoid repetition. For example, if you are writing a report and have used "not do" several times, you could mix it up by using "refrain from" or "abstain from" instead. These synonyms also have slight differences in meaning, so it is important to choose the most appropriate phrase for the situation.