Forward-stimulated Raman scattering can be used to combine multiple broad-band pump beams into a single coherent Stokes wave. In this paper, the equations of motion for the Stokes electric field are derived in the presence of multiple pump waves propagating at slightly different angles with respect to the Stokes propagation direction. The solutions with pump depletion are presented for fully coherent pump waves. It is shown that the Raman gain is lower for incoherent pump waves than for coherent pump waves. Stokes field solutions are used to evaluate the far-field intensity of the Stokes output from a saturated Raman beam combiner. It is shown that the condition for coherent combination depends on the beam diameter, pump coherence length, and the angle between the pump and the Stokes. It is also shown that multiaxial mode Raman shifting can generate Stokes waves with higher beam quality than the pump waves, both with phase perturbed or highly distorted pump beams.