Electronic structure methods for hot, dense plasmas often use density functional theory (DFT) with major additional approximations.  For example, orbital-free DFT currently uses functionals that do not recover discrete core states, while average atom methods model one atom in an averaged plasma.  Here we use the so-called multiple scattering method to solve the Kohn-Sham DFT equations for dense plasmas.  The method is all-electron and does not use pseudo-potentials.  We find that equation of state calculations result in good agreement with other state-of-the-art methods, and find that computational cost does not increase with temperature, allowing access to very high temperature, non-degenerate systems.