Or pry the door frame apart and tap it back in place after rolling the rack out.
Worth a mention as many door frames are easier to remove than a number of people might suspect .. fewer pieces to disassemble than many {object}'s and not an uncommon hack when moving furniture.
Removing door frames is easy. Putting it back together without looking like crap is the hard part.
Repeat after me: caulk and paint make it what it ain't