The phrase "enter into" is commonly used in various contexts. It generally means to begin or set foot into something. However, there are several alternative terms that can be used instead of "enter into," depending on the context. For instance, in legal terms, one can "execute" a contract or "sign" an agreement. In technology terms, someone can "access" a system or "log in" to an account. In literary terms, an author can "penetrate" the depth of a character's mind or "immerse" the reader into the story. Other synonyms for "enter into" include "engage," "partake," "commence," "initiate," or simply "start." Overall, using different terms can add variety to one's writing or conversation and strengthen the meaning conveyed.