Is it possible that the DC3 was designed to have two passenger doors at the rear of the fuselage - in other words customer option such as one on the left OR right or both left and right?
Exactly right. The launch customer, American Airlines (1935) ordered the right-side door, and Wright Cyclone engines. Shortly after, United Airlines ordered the left-side door and P&W Twin Wasp engines.
Other customers (Capitol, Delta, export customers, etc.) ordered various combinations of the above.
Early 60s, I recall Lake Central Airlines ships all were P&W power, but some ships had R/H doors, some were L/H.
EDIT: Doors on both sides? It's possible of course, although I'm not aware of the need for this option...