I believe for the moment the only thing you can do is
Separate your volume
Modify each surface without (or not) move) "common points" depending of result wished )
Join when all surfaces are modified
here with only one surface of a cube...
Hi glmr, sorry no currently there isn't a Cage Edit function in MoI. It is something that I want to add in a future version though.
It is possible to use the Flow command to do some similar types of deformations, for example here's a flow from a base plane to one that has had its control points narrowed at the top: