  Considering Schur positivity of differences of plethysms of homogeneous
symmetric functions, we introduce a new relation on integer partitions. This
relation is conjectured to be a partial order, with its restriction to one part
partitions equivalent to the classical Foulkes conjecture. We establish some of
the properties of this relation via the construction of explicit inclusion of
modules whose characters correspond to the plethysms considered. We also prove
some stability properties for the number of irreducible occurring in these
modules as $n$ grows.
