Cage edit command that can adapt to any form automatically

Is there any chance to have cages with controlpoints x,y,z that do not start as a box, or that can be deformed before and without applying the deformations to the child? I know that is possible with surfaces as cage, but they have only U and V points.
I suspect this is fundamentally not possible, but I am not sure. This is a very old wish of me.

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