Via Facebook. X-15B illustration, cutaway and drawing, and flight profile (with crew ejection). Exposition from the Osprey XPLANE edition on the X-15:
"This enlarged, two-man version of the X-15 was part of Gen Curtis LeMay's plan to ensure that a USAF pilot would be the first man in outer space, expressed in Project 7969..." ... "The two Navaho booster stages would have taken the X-15 up to 400,000ft, from where it could accelerate to 18,000mph under its own power, make three Earth orbits before re-entry and return to Edwards, or possible crew ejection over water." (page 74 of XPLANES North American X-15 by Peter E. Davies )
The illustration here seems to show three Navaho rockets being employed though. Otherwise, the X-15 would have had a more powerful engine - the 75,000lb thrust XLR-105, a thicker Iconel-X skin, and/or the addition of various other advanced materials (one idea was to utilize the more heat-resistant Rene-41 alloy).