We conduct numerical and experimental investigations on Kerr comb generation in a nonlinear and non-reciprocal fiber cavity by leveraging both stimulated Brillouin backscattering and cascaded four-wave mixing. By engineering the net cavity dispersion to be either normal or anomalous, we enable the formation of diverse patterns and localized structures in the cavity field. The comb’s properties depend crucially on the mismatch between the frequency spacing of the bichromatic pump and the free spectral range of the Brillouin laser cavity in both cases. Particularly, in the anomalous regime, adjusting this parameter yields coherent, stable frequency combs in the modulation instability regime. This allows control and expansion of the spectral bandwidth up to 2 THz in normal dispersion and to 6 THz under anomalous net dispersion. This versatile and easily reconfigurable method holds potential for applications in high-speed communications and microwave synthesis.