Recently, we introduced a new switching-off technique applicable to subdiffraction-limited coherent Raman imaging, where a coherent anti-Stokes Raman scattering (CARS) signal can be selectively suppressed via competitive stimulated Raman scattering (SRS) processes between vibrational modes of a single molecular species. Here, we show that such a three-beam CARS suppression can be made via double SRS processes between vibrational modes of heteromolecular species, a mixture of paraffin oil and benzene. We achieve more than 80% suppression of the pump-Stokes-beam CARS signal for the ring-breathing mode (target mode) of benzene when the C-H stretching mode (acceptor mode) of paraffin oil is used to deplete the pump photons via the pump-depletion-beam SRS process. The freedom in the choice of acceptor mode for depletion, which could be a critical advantage of the present switching-off scheme, can be of use for overcoming current challenges of depletion-based super-resolution coherent Raman imaging of biomolecules.