  Motivated by viewing categories as bimodule monoids over their isomorphism
groupoids, we construct monoidal structures called plethysm products on three
levels: that is for bimodules, relative bimodules and factorizable bimodules.
For the bimodules, we work in the general setting of actions by categories. We
give a comprehensive theory linking these levels to each other as well as to
Grothendieck element constructions, indexed enrichments, decorations and
algebras.
  Specializing to groupoid actions leads to applications including the plus
construction. In this setting, the third level encompasses the known
constructions of Baez-Dolan and its generalizations, as we prove. One new
result is that that the plus construction can also be realized an element
construction compatible with monoidal structures that we define. This allows us
to prove a commutativity between element and plus constructions a special case
of which was announced earlier. Specializing the results on the third level
yield a criterion, when a definition of operad-like structure as a plethysm
monoid -- as exemplified by operads -- is possible.
