  Unstable operations in a generalized cohomology theory E give rise to a
functor from the category of algebras over E to itself which is a colimit of
representable functors and a comonoid with respect to composition of such
functors. In this paper I set up a framework to study the algebra of such
functors, which I call formal plethories, in the case where $E_*$ is a Pr\"ufer
ring. I show that the "logarithmic" functors of primitives and indecomposables
give linear approximations of formal plethories by bimonoids in the 2-monoidal
category of bimodules over a ring.
