When it comes to finding a suitable synonym for "shack up with," there are a few alternatives you can use depending on the context. "Move in with" or "cohabit with" are two commonly used phrases with similar meanings to "shack up with." Alternatively, you could use "share a living space with" to be more precise about the nature of the arrangement. Another option is to use "room together" which suggests a more temporary living situation, such as sharing a hotel room or a dormitory. Ultimately, the choice of synonym will depend on the tone and formality of your writing as well as the specific context in which the phrase is being used.