We investigate experimentally and theoretically few-particle effects in the optical spectra of single quantum dots (QDs). Photo-depletion of the QD together with the slow hopping transport of impurity-bound electrons back to the QD are employed to efficiently control the number of electrons present in the QD. By investigating structurally identical QDs, we show that the spectral evolutions observed can be attributed to intrinsic, multi-particle-related effects, as opposed to extrinsic QD-impurity environment-related interactions. From our theoretical calculations we identify the distinct transitions related to excitons and excitons charged with up to five additional electrons, as well as neutral and charged biexcitons.