Effects of semi-classical plasma on the doubly excited singlet S states of Ps^- have been investigated. The effective interaction potential in semi-classical plasmas is modelled by a pseudopotential containing two adjustable parameters: screening parameter μ and the de Broglie wavelength of the pair of interacting particles λ. The parameter μ takes care of the collective screening effect, whereas the parameter λ describes the quantum mechanical effect of diffraction at short distances. An extensive highly-correlated Hylleraas-type wavefunction containing 715 square integrable functions with a scaling parameter is employed in the stabilization method to identify the doubly excited states (DESs). The energies and the widths of the DESs are then calculated by fitting the density of the resonant states with the Lorentzian profile. Convergence of the energy and width of each identified state is corroborated by increasing the number of terms in the employed wavefunction. For the plasma-free case, we have been able to identify four DESs lying below the Ps (n=2) excitation threshold. Computed energy and width of those states are in excellent agreement with some reliable results in the literature. An inclusive study is then made on the changes in the energy and width of these states subject to the variation of μ and λ. Our findings reveal that energies of the DESs increase with respect to the increasing λ at a given μ. However, variation of the width with respect to λ at a given μ is distinctive. We hope that our findings of this paper will provide fruitful information to the research communities in plasma physics, atomic physics and astrophysics.