The high resolution photoluminescence spectra reported here reveal new details of the structure of both bound excitons and bound multiexciton complexes in donor and acceptor doped Si. The bound exciton and bound multiexciton complexes in Si containing P impurities are found to have excited states, as was postulated in a recent shell-model of the bound multiexciton complexes. Several new features of the luminescence due to bound excitons and bound multiexciton complexes in acceptor doped Si are also found to be in agreement with the shell-model. In contrast to previous studies, we find no reason to doubt the original bound multiexciton complex explanation of the luminescence line series which are seen in lightly doped Si. The implications of these results are also discussed in relation to previously reported interpretations of the photoluminescence spectra of donor-doped Ge.