Multistate protein design explores side chain mutations, with the backbone allowed to sample a small, predetermined library of conformations. To achieve Boltzmann sampling of sequences and conformations, we use a hybrid Monte Carlo (MC) scheme: a trial hop between backbone models is followed by a short MC segment where side chain rotamers adjust to the new backbone, before applying a Metropolis-like acceptance test. The theoretical form and a practical approximation for the acceptance test are derived. We then compute backbone conformational free energies for two SH2 and SH3 proteins using different routes and protocols, and verify that for simple test problems, the free energy behaves like a state function, a hallmark of Boltzmann sampling.