The phrase "tied up with" refers to being busy or occupied with something. However, there are several other synonyms that can be used instead of this phrase. For instance, you can use words like "engaged", "involved", or "preoccupied" to convey the same meaning. Additionally, words like "consumed", "absorbed", and "wrapped up in" can be used interchangeably with "tied up with". These synonyms can be used in various contexts, such as work, family, or hobbies. By using different words, you can add more variety to your language and avoid repeating the same phrase over and over again.