The phrase "engaged in" typically refers to being involved or actively participating in something. There are several synonyms that can be used in its place for a more varied and descriptive way to express this idea. These could include "occupied with," "involved in," "immersed in," "busy with," "committed to," or "working on." Depending on the specific context, other options may be more appropriate. For example, "entangled in" could be used to convey a negative connotation of being caught up in something complicated or difficult. Overall, using synonyms for "engaged in" can help to enhance language and make communication more effective.