The T-38 Talon is soldiering on in its fifth or sixth decade as the USAF's only supersonic trainer. There was a time, though, when Northrop Grumman suggested it could be much more - a suborbital Mach 3.2 trainer capable of hitting 250,000 feet, where its control surfaces would be useless and student pilots would control it with hydrogen peroxide thrusters. As often happened in the anything-is-possible 1960s, there were ideas for even more way-out versions. Amazing.
UPDATE: This one was so interesting I sent it to friends who were T-38 instructor pilots. Their responses:
Chas Ruth: "Would I want to fly it? Hell, yes! Do I think it would work? Probably not."
Elizabeth Knemeyer Ruth: "I'm not an engineer, so I don't know if they could make it work. But it would certainly be a blast to give it a try."