A theoretical analysis is presented for the stimulated Raman scattering (SRS) driven by multiple beams with certain frequency differences or bandwidths. The concomitant electrostatic modes are excited by the scattering lights when the pump beams share a common electron plasma wave to drive SRS. This coupling can be suppressed when the frequency difference of the two beams is three times larger than the SRS growth rate of a single beam, where the beams develop their scattering lights independently. To mitigate SRS further under the multibeam irradiation, polychromatic pumps are introduced to reduce the SRS saturation level, where the weakly coupled common modes are heavily damped in hot plasmas. The sidescattering driven by polychromatic light in inhomogeneous plasmas is significantly reduced due to the wavevector mismatch of daughter waves. Particle-in-cell simulations confirm our theoretical analysis and demonstrate that the strength of multibeam SRS and the hot electron production in inhomogeneous plasmas can be controlled at a low level by polychromatic light with a few percentage bandwidth (), even in the non-linear regime.