The phrase "got busy with" is commonly used to indicate that someone is occupied with a task or activity. However, there are numerous synonyms to express the same meaning. Some alternatives include "engaged in," "involved in," "immersed in," "buried in," and "caught up with." Other similar phrases could be "tied up with," "occupied with," "preoccupied with," or "distracted by." Each of these phrases can help to convey a slightly different tone or nuance, depending on the context and intended meaning. As a writer, it's always helpful to have a variety of synonyms in your vocabulary to avoid repetition and add richness to your language.