A cage can be created and then deformed before being used as a control object.
Cage command (not CageEdit) to create a cage with desired number of control points in each direction.
Modify the cage to the desired shape. Turn on control points if needed and move control points.
CageEdit command. Select the object to be modified as the captive object. Select the Cage created previously as the control object. (Click on the existing cage. Do not create a new cage.) Alter the cage as desired and the captive object with be modified.