Other ways of saying "set up shop"?

“Setting up shop” is not necessarily unwelcome. It merely means occupying a position or role and getting organised to perform the relevant activities.

Other idioms that may contain a hint of disapproval are:

“Making yourself at home”: could be a response to a genuine welcome, or might be considered as a presumptuous occupation of a place that others might need.

“Getting your feet under the table”: probably a less welcome thing, suggesting an over-familiar occupation of a role or place. It is an analogy based on the idea that you have insinuated yourself into a place where you did not originally belong and that, now sitting at the family table, you are enjoying the food and resources (economic, emotional or perhaps sexual) of the family life.

Wear out one's welcome may convey the idea:

to be no longer welcome to stay in a place because one has stayed too long, been impolite, etc.

(M-W)

Where I come from, unwanted visitors are called squatters. As in: "The campers squatted on my land without permission, so I had to call the police."