Quantum superchannels are maps whose input and output are completely-positive trace-preserving (CPTP) maps. Rather than taking the domain to be the space of all linear maps I motivate and state a new definition of superchannel acting on the operator system spanned by CPTP maps. Arvesons extension theorem allows us to show that a Stinespring-like characterisation theorem for superchannels applies to this class of maps. I then discuss some implications of this new approach and how it differs from the usual definition.