There are several synonyms for the phrase "dig into". One could say "delve into" to convey a deeper level of exploration or investigation into a subject. "Scrutinize" or "examine" can also be used to imply a thorough analysis. "Probe" and "penetrate" may be suitable when discussing difficult or sensitive topics. "Explore" can be utilized in a more general sense, to convey a sense of curiosity and discovery. Finally, "digress" can be used when straying from a main topic or point of discussion. Overall, there are a multitude of synonyms available to use in place of "dig into" depending on the context and intention of communication.