Synonyms for Move in:

n.

occupy, take occupancy, reside, settle down, populate, settle, board, inhabit, squat, get a home, live, come from, establish. come up, go over, make for, advance, make toward, approach, creep up on, gain on, bear down, near. move in (noun)
draw in, get in.

v.

enter (verb)
get in.
motion (verb)
draw in, get in.

Other synonyms:

Other relevant words:
inhabit, occupy.