looks ab bit like their proposals from the Space Launch Initiative (SLI) from around 2000:
(image from here)
This makes me wonder if once operational the design could be 'stacked' into a bimese vehicle to give a bigger payload? Alternatively an enlarged version (XS-2?) could be used as threbasis of a TSTO, with an uprated XS-1 as the upper stage. Other options for an upper stage could be derived from the X-37 or Dreamchaser designs.