"Keep busy" is a phrase often used to describe the act of staying occupied and engaged in a variety of tasks and activities. However, there are many other ways to express this idea. Some synonyms for "keep busy" include "stay active," "remain productive," "keep occupied," "be engaged," "stay on task," "busy oneself," "distract oneself," "occupy oneself," and "keep oneself busy." Each of these phrases implies a similar idea of staying active and engaged, but with slightly different connotations and nuances. Using a variety of synonyms can help to avoid repetition and keep your language fresh and interesting.