extend a B-surface with the same parameterization?

To my knowledge, Curve Length is for extending a curve, and Extend Sheet is for extending a surface. But it seems that they work in completely different ways.

Curve Length (Natural) extends a curve with exactly the same parameterization.

Extend Sheet extends a surface in diffrent ways:

• Natural Curvature >>> Extends a B-surface with a small area that is curvature continuous at the boundary, and then tangent beyond that area.

• Tangent >>> Extends a B-Surface tangent from the boundary.

I wonder whther it's possible to extend a B-surface with exactly the same paraterization just as Curve Length works with a curve.

Thanks!