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Motivated by viewing categories as bimodule monoids over their isomorphismgroupoids, we construct monoidal structures called plethysm products on threelevels: that is for bimodules, relative bimodules and factorizable bimodules.For the bimodules, we work in the general setting of actions by categories. Wegive a comprehensive theory linking these levels to each other as well as toGrothendieck element constructions, indexed enrichments, decorations andalgebras.  Specializing to groupoid actions leads to applications including the plusconstruction. In this setting, the third level encompasses the knownconstructions of Baez-Dolan and its generalizations, as we prove. One newresult is that that the plus construction can also be realized an elementconstruction compatible with monoidal structures that we define. This allows usto prove a commutativity between element and plus constructions a special caseof which was announced earlier. Specializing the results on the third levelyield a criterion, when a definition of operad-like structure as a plethysmmonoid -- as exemplified by operads -- is possible.

Plethysm Products, Element and Plus Constructions