There are various synonyms for the phrase "bound up in," which means deeply involved or connected with. Some of these synonyms include engrossed in, absorbed in, immersed in, occupied with, preoccupied with, tied up with, caught up in, and involved with. These phrases can be used interchangeably based on the context of the sentence. For instance, if someone is engrossed in a book, it means that they're wholly involved in reading it. Similarly, being caught up in something could mean that you're involved or consumed by it, whether it is a task or an emotional state. Regardless of the synonym used, each highlights a deep connection or a strong focus on something.