We investigate polymer partitioning from polymer mixtures into nanometer size cavities by formulating an equation of state for a binary polymer mixture assuming that only one (smaller) of the two polymer components can penetrate the cavity. Deriving the partitioning equilibrium equations and solving them numerically allows us to introduce the concept of polymers pushing for the action of nonpenetrating polymers on the partitioning of the penetrating polymers. Polymer partitioning into a pore even within a very simple model of a binary polymer mixture is Shown to depend in a complicated way on the composition of the polymer mixture and/or the pore penetration penalty. This can lead to enhanced as well as diminished partitioning, due to two separate energy scales that we analyze in detail.