The "captain in the right-hand seat" discussion got me thinking. As of 2013, you need an ATPL to operate any plane operating under Part 121 (as part of an "airline"). Both Captain and FO need this level of license, and new Captains require at least 1000 hours as FO.
However, all you'd need to fly the same model of plane for hire in any other situation is a CPL and the applicable type rating for the aircraft. Prior to 2013 that was all you needed to be hired as an FO on an airliner and get yoke time towards your ATPL and the left-hand seat.
The question is, are there still opportunities for a civilian CPL holder to fly large turbofan-powered airframes for a living on his way to an ATPL? My first thought was freight, but cargo planes for FedEx or UPS operate under Part 121, same as American Airlines. The only thing that really leaves is charter flights, which operate under Part 135 and thus may not require the same stricter regs as a pilot on a scheduled service. But, I don't know how many charter operations are using anything bigger than a narrow-body.