<Reusable kerosene rocket engine

Kerosene is jet fuel, so both the rocket and the jet engines could run off the same fuel tank. Kerosene is also routinely stored in the wings of aircraft which gives them greater cargo capacity and superior aerodynamics, whereas liquid hydrogen cannot be stored in the wings.

As a technology demonstrator a specially modified tail-less C-17 Globemaster could carry an Aerograppler to an altitude of 33,000 feet and release it. The Aerograppler would fire its kerosene rocket to propel it to the edge of space. Then it would glide down and rendezvous with the same C-17 Globemaster. Upon approach it would feather its wings outward and fire up its kerosene-fueled, airbreathing jet engine, to allow it to match speed and to maneuver. It would dock with the C-17, perhaps even exchange a payload. Most importantly, it would be refueled by the C-17 in the air (kerosene & liquid oxygen). Then it would fly away from the C-17, feather its wings back and fire its kerosene engines, once again propelling it to the edge of space.

This routine could be repeated over and over again, as long as the C17 had onboard supplies of kerosene and liquid oxygen. Until then, the Aerograppler would never have to land. Theoretically a second C-17 Globemaster could fly up with fresh fuel onboard and relieve the first, which would land on a runway. Eventually, the Aerograppler would land. It could conceivably do this two ways:

It could glide to a landing on a runway, OR it could land on top of the C-17, dock with it using special grappling systems, and piggyback the C-17 to a runway landing. I personally prefer the latter, but it would obviously have to be capable of either scenario because things do go wrong.