If you want to draw a box on top of an existing box, simply snap to a point on top of the existing box during drawing. The working plane offset is automatically adjusted to a snap point on top of the existing box.
While in draw box mode, press the Ctrl key to see the snap points. Position your cursor near the center of the top face and click once.
Draw the new box on top of the existing box. Note that the working plane offset changes for you.