We have performed an exact diagonalization of the exchange Hamiltonian of a finite, 16-spin model of bcc **3He consisting of two interpenetrating cubes with periodic boundary conditions, for competing three-spin and planar four-spin exchange. Quantum effects are found to be much larger (up to 100% in ground state energy) than with pure Heisenberg exchange. However, the phase diagram has qualitative similarities with the mean field result. The comparison between theory and experiment is examined in light of the present results.