An existing equilibrium partitioning model for calculating the equilibrium gas/particle concentrations of multiple semi-volatile organics within a bulk aerosol is extended to allow for multiple core aerosol modes of different sizes and chemical compositions. In the bulk aerosol problem the partitioning coefficient determines the fraction of the total concentration of semi-volatile material that is in the condensed phase on the aerosol. This work modifies this definition for multiple polydisperse aerosol modes to account for multiple condensed concentrations; one for each semivolatile on each core aerosol mode. The pivotal assumption in this work is that each aerosol mode contains a core constituent which is involatile thus overcoming the potential problem of smaller particles evaporating completely and then condensing on the larger particles to create a monodisperse aerosol at equilibrium. The resulting coupled non-linear system is approximated by a simpler set of equations in which the organic mole fraction in the partitioning coefficient is set to be the same across all modes. By perturbing the condensed masses about this approximate solution a correction term is derived which accounts for much of the removed complexities. This method offers a greatly increased efficiency in calculating the solution without significant loss in accuracy, thus allowing its inclusion into large scale models feasable.