I would like to know if I can Project Curve on Surface (Nurb) and then be able to use that curve as a manipulation tool. That was probably terrible wording.

I want to project say a circle shape onto a cube and then be able to select that circle shape and push and pull it like an Isoparm or Edge to reshape the cube. Is this doable? Right now I can only seem to be able to project the curve and then perform a Trim (which is cool, but not what I'm looking for) or reposition the curve on the surface by selecting and moving it.

Thanks!