This seems to be pretty much it… in case you found anything else “shiftable”, put the link in the comments!
Shiftable Wall TVs (Base Game and Late Night)
Shiftable Store Stuff (& More!)
Shiftable Paintings, Easel Paintings & Wall Lights
Shiftable Mirrors Base Game + Expansion Packs
Shiftable Cabinets & Columns & Beams