  It is known that the Grothendieck group of the category of Schur functors is
the ring of symmetric functions. This ring has a rich structure, much of which
is encapsulated in the fact that it is a "plethory": a monoid in the category
of birings with its substitution monoidal structure. We show that similarly the
category of Schur functors is a "2-plethory", which descends to give the
plethory structure on symmetric functions. Thus, much of the structure of
symmetric functions exists at a higher level in the category of Schur functors.
