It looks to me that when cannon were just getting popular, gunners were already juiced up to get more than one shot off before reloading. There seems to be many ways to get there also, as this 3 shot experimental cannon from Henry the VIII's time, now in the Royal Armouries, took the volley gun approach.
The gun that really gets me going though is this 3 shot revolver cannon. I found this picture on Wikimedia Commons, and am not quite sure what or where it came from, but suspect it's in France somewhere, and possibly in the 1952 film, Hôtel des Invalides. If so, it's probably in the Musée de l'Armée. Very unique gun!