Yes and no. You can't cockpit jumpseat, but you can cabin-only jumpseat on any US airline Mesa has a reciprocal jumpseat agreement with, subject to the appropriate taxes/fees.

If you encounter the wrong gate agent, UAL/Airways might give you a hard time about why you aren't in the non-rev system. And foreign gate agents are notoriously bad at even comprehending what "jumpseat" means, but it's doable if you know what you're doing and how to explain it.

Additionally, some of our jumpseat agreements are restricted to "number of cabin jumpseaters limited to number of cockpit jumpseats installed in a/c." So, for example, if it's a 757 w/2 cockpit jumpseats, they might only allow 2 cabin jumpseaters total from all airlines.

I've ridden in the back on Polar/Atlas, Delta, Continental, and even an NWA cargo 747 in the past--if there is a "cabin" separated by the cockpit by a secure door (with the exception of FDX/UPS, due to their policies), you can jumpseat in the cabin internationally.