Monopoly Deal - Can you switch your cards after charging rent on them?
The original rules state that


  [y]ou can move a wild card around between sets on any turn. This does NOT count as one of the 3 cards you can play per turn (as it's already on the table).


and


  [i]f you replace a wild card with a property card of the right colour and can't use it as part of another set leave it in your property area - you might need it later! 


The rules appear to presume that all properties of the same colour are always placed together.

The first rule allows you to move the wild card (double or rainbow) between two sets, presumably only if in legal positions.

The second implies that if you can put a wild card into a set, you must put it into a set.

While you can move a wild card out of a complete set to an incomplete set, you cannot move the wild card from any set to be alone.