  Quantum superchannels are maps whose input and output are quantum channels.
Rather than taking the domain to be the space of all linear maps we motivate
and define superchannels on the operator system spanned by quantum channels.
Extension theorems for completely positive maps allow us to apply the
characterisation theorem for superchannels to this smaller set of maps. These
extensions are non unique, showing two different superchannels act the same on
all input quantum channels, and so this new definition on the smaller domain
captures more precisely the action of superchannels as transformations between
quantum channels. The non uniqueness can affect the auxilliary dimension needed
for the characterisation as well as the tensor product of the superchannels.
