a sheet of thin-flexible material (like paper) being folded over into a loose fold?
This could possibly be better accomplished by using bones. (figure mode), if you're keen to give that a try.
Morphs are absolutely awesome for a lot of stuff, but a possible problem with 'folding a piece of paper' using morph targets is that they tend to take the straightest line, so getting the 'arc' effect when folding something over won't always work out.
Bones, however, arc nicely, and more perfectly suited to what you're suggesting.
When you make your 'thin plastic sheet', remember to allow enough points for the bones to hold on to. ie: use 'weights' rather than influences when given the option, and understand that when 'painting weights' in figure mode, its the points that get attached to the selected bone.
Check out the manual for basics of animating in figure mode. (chapter 5. Figure editor)
Although mostly dealing with 'influences', there is a short section on painting weights at the end of the chapter, and it does explain the 'gist' of how bones are used to animate objects.
Good luck, sounds like you're learning some stuff. I would suggest to 'give bones a go', and let us know how things are working out.