The phrase "may not" indicates a possibility of an action not taking place. Synonyms for "may not" include several phrases that convey a similar meaning, such as "might not," "could fail to," "be unable to," "not have permission to," "be prohibited from," "lack the ability to," "fall short of," "be restrained from," "not be authorized to," "be disallowed," "not be permitted," and "cannot." These alternative phrases can add variety to your writing and help emphasize the probability of certain actions not taking place. It's essential to choose the synonym that conveys the meaning you intend to deliver.