One of the coolest features of The Sims 3 is that neighbors can not only be visited, but they might ask YOU to move in with THEM.
But I have never seen this happen. S3PE reveals why! The chance of an NPC asking you is 1%. The chance when you are in a romantic relationship is 3%. By that time you probably already asked them to move in with you.
I changed it! Now the chance of them asking during conversation is 10%, and when romantic, 25%. They'll wait 2 days between asking if you say no, so you won't be constantly bombarded by requests. Note that denying the request gives a -10 drop in relationship.