If you're looking for a way to express a deep and intense engagement with something, there are plenty of synonyms for the phrase "sink one's teeth into." One option might be "dig in," which conveys a sense of determination and focus. Another choice could be "get stuck into," which suggests a more active involvement and a willingness to really dive into a project or activity. If you're looking for something a bit more aggressive, "chew on" is a good option, as it implies a level of tenacity and persistence. Ultimately, the choice of synonym depends on the specific context and the level of intensity you want to convey.