The topology of a block can be edited using the Add surface tool which allows you to modify a block surface by drawing a perimeter on an existing block surface and dragging it inwards or outwards along an axis, normal to the surface. It is a special case of the Drag block face tool which is used to drag a whole face. Add surface allows you to drag a portion of a block surface creating a new block topology.
To use the Add surface command:
See also the Add surface, increment snaps tutorial