Can an object be automatically cloned using an action button

Not sure if this is possible - I need to do more than just clone an object.  I'd like to put an image/object into a pdf and make it so the user can click on the object and automatically have a clone, then drag the clone anywhere on the page.  The original object would stay where I placed it but an indefinite numbers of copies can be created from the original.  This is possible on the "whiteboard" programs, is this possible in any of the adobe programs?