We present an overview of the model we developed (F. P. Laussy et al., cond-mat/0505728 [1]) to describe strong coupling of light with excitons hosted by large quantum dots, where the number of excitons is eventually limited by Pauli blocking of the underlying electron-hole structure. We apply it to a limiting case not investigated before, where excitations are created in states analogous of Dicke states describing non-interacting distinguishable fermionic excitations coupled through the radiation field. The multiplet structures in the optical emission spectra which we obtain show, by comparison with our previous results, that they remain essentially the same independently of the model for small saturation numbers, while they acquire specificities of their own when the number of allowed excitons becomes large.