As the old saying goes, "there's nothing new under the sun.", but looking thru my Flayderman's Guide I only see one multiple cylinder pistol.
This gun is the Elgar & Smith 9 shot revolver/Volley gun/Pepperbox.
It has three barrels attached together and to the pistols frame.
It has three, three shot cylinders with the chambers located in a triangular pattern that matches the three barrels.
Each of the three shot cylinders has one percussion cap which fires all three chambers in a cylinder simultaneously.
Once the shooter has fired his 3 shot cylinder he rotates the next three shot cylinder to align with the three barrels and he is ready for his next shot.
The only other multiple loaded chamber guns shown do not have multiple cylinders. Rather, they have very long cylinders and the chambers are double loaded. That is, each chamber is loaded with powder, ball, powder, ball.
This in effect makes a 5 chamber gun like the John Walch Double Hammer Pocket revolver a 10 shot gun.
Another double loaded pistol is the John Walch Navy Model 12 shot Revolver which had 6 chambers.
I have seen photos and drawings of multiple cylinder Flintlock pistols but they were very rare and seem to be a one of one production.