We investigate the dependence of a single-generation galactic mass function (SGMF) on variations in the initial stellar mass functions (IMF) of stellar clusters. We show that cluster-to-cluster variations of the IMF lead to a multi-component SGMF where each component in a given mass range can be described by a distinct power-law function. We also show that a dispersion of ≈0.3 M_⊙ in the characteristic mass of the IMF, as observed for young Galactic clusters, leads to a low-mass slope of the SGMF that matches the observed Galactic stellar mass function even when the IMFs in the low-mass end of individual clusters are much steeper.