You can make that in Moi ! ; (before maybe some deformations's cage or other marvelous things! ;)

But all surfaces must be Separated : moving tweaking points can be on several surfaces on the same time!
So for a cube don't move it's edges if you want keep it as a solid when you Join surfaces at the end of tweaking!

Thanks Pilou for opening my eyes to this! Separating to surfaces and then playing with points that belong to different surface and then joining can be a great way to deform a solid in a very controlled way.