Prevent surface from stretching

I am interested in creating forms with overlaps and folding using the forked surfaces. However, when doing so on Rhino, the surface stretches and warps, like it does on the image below, on the left.
In real life - physically - overlapping as an operation would be feasible, with a sheet of paper / thin material without stretching. Are there any ways to keep the surface “locked” so it stays as a single curved surface?

20.06.15_overlapping.3dm (268.9 KB)

What commands did you use to deform the surface?

One approach: Split the forks into separate surfaces. Create a new surface with the shape you want to bend the original surface(s) into. Don’t worry about the boundaries, just get the shape. The shape will need to be “developable” - for instance a section of a generalized cylinder or cone. Once you have the shape then UnrollSrf that shape to be flat. Position the “sheet of paper” surface you want to be rolled over the flattened surface. Use FlowAlongSrf to deform the “sheet of paper” surface to the shape.

To create a generalized cylinder first create a curve and a line. Then ExtrudeCrvAlongCrv to create the cylinder.

To create a generalized cone first create a curve and a point which will be be the apex of the cylinder. Then Loft between the point and curve.