Indeed it is possible, although company policy states that people shouldn't be allowed to stay in the cockpit. It highly depends on the crew. Three months ago I flew with KLM from AMS to MAD on a 737. When I told the captain that I was a PPL holder and studied to get my ATPL I was allowed stay on the jumpseat the hole flight. A great experience especially the ldg at MAD.
So I would say Godbless, when you are about to fly KLM just try it.