I would like to be able to extrude through an exiting body as cut and be able to retain the cut material as a new body. This would be handy for sub-dividing a single body into a number of smaller bodies.
To do this operation currently I have to duplicate the body using a rectangular pattern (with pattern distance of zero), then perform a cut extrusion on the first body and a combine extrusion on the second body. This works OK, but it is three steps and it could be done in one step.
From a UI perspective, implementing this would only require the addition of a check box on the cut and combine extrusion types to retain the cut material. In each case the cut material would become the new body, so choosing either the cut or combine method would enable you to choose which part of the body retains the original body name.