You'd want to take it off first. Sometimes you discover real clapboards in excellent shape underneath and wonder why someone plastic coated their house.

I'm not a professional, but ... no. For a couple of reasons. Here's one: Vinyl siding has slotted nailing flanges that allow the siding to expand and contract as the temperature changes. If you were to nail new siding over the old siding it would be impossible to hit the flanges in the old siding - so you would be nailing the siding tight to the house and preventing it from being able to expand and contract freely. That would make the old siding buckle, resulting in the new siding buckling too. Another problem would be flashing the new siding at windows and trimming at corners. Just not a good idea.