You can physically move it wherever you want, but you have to hope that there is an opening available in the "cell" at the new location, otherwise, you've got a paperweight.

Each Dishy is assigned to a specific ground station, so you can freely move it around as long as it's 'close enough' to that ground station. (I don't know the distance by memory..) There's a way to ask Starlink to switch your ground station, which is what people with the RVs are doing.