Command like project and pull?

I would like to project a parametric design onto a cube, although the project and pull commands only project onto the one surface that aligns with the parametric design.

I would like the parametric design to fold over the top of the cube, not just stick to one surface. as if the parametric design is made of sharan wrap and I’m folding it around the cube like I’m wrapping it.

I don’t mind if it distorts the outcome.