B767 Captain reported after shutdown and setting the parking brake; aircraft started moving resulted in loss of control on the ground.

Narrative

We were assigned ZZZ recovery with a XA:00 local show. The flight to ZZZ was uneventful. Upon landing the left engine was shut down after the appropriate cooling period; and the remainder of the taxi to park was single engine with APU running. The marshaling crew was visually identified; and the aircraft entered the parking area. The marshaler on the nose had one wand that was not illuminated. Although this was a distraction; I do not feel it had any factor in the following event. At the appropriate position; the lead marshaler gave the cross-wand symbol and I stopped the aircraft. I immediately pulled up on the parking brake lever and recall the amber Parking Brake light illuminating. I then shut down the right engine and moved my hand to the red anticollision light to extinguish it once the right engine had spooled down to a safe rotation speed. It was at that point that I perceived relative motion of what I thought was the stairs coming to the aircraft; but quickly determined the aircraft was moving; not the stairs. I immediately stopped the aircraft a second time. Once the ground crew placed the stairs in their proper location; I immediately exited to check the welfare of all those on the ground; and then to ascertain if the aircraft had contacted any equipment; etc. Thankfully; everyone on the ground was unaffected and the aircraft did not hit anything.