Integer and text properties can be set to anything using an equation, but the other 6 property types can only be set to a constant.
They should be able to be set to an %object%, %character% or %location% reference if of appropriate type.
It should also be possible to set any property to the same value of any other property of the same type.
(For state lists the two state lists would have to be identical to be considered the same type)
Where the set Integer/Text properties has a button to toggle between a variable or an expression, the other types could have a button to select the existing drop-down list or one of Character/Object/Location followed by two drop-down lists to select the source item and source property (but limited to properties of the same type as the destination property).