This method works in the same way as 
on an open curve, but you must define a reference axis. Before the reference axis is used, it is projected onto the principal plane.
Define a suitable reference axis. In this example, the surfaces will fail to morph with a vertical axis. This is because when you define the plane that is normal to the reference axis, it goes through the reference curve more than twice for some points on the surfaces to be morphed.
For this example, use a horizontal axis. No plane normal to this axis crosses the reference curve more than twice.
This example gives the following result.
