Graphene's unique gapless band structure and remarkably large third-order optical susceptibility have drawn significant attention to its nonlinear optical response, particularly in the context of coherent anti-Stokes Raman scattering (CARS). Under the combined influence of phononic and electronic resonances, the CARS response of graphene has been observed to exhibit a distinctive feature of time-resolved dip-to-peak evolution. Here, we report a greatly enhanced double resonance Raman mode beyond the G mode of multi-layer graphene with broadband CARS measurements. The significant difference in the intensity ratio between CARS and SR for this mode may be attributed to the preferential activation of low-frequency phonons in the impulsive stimulated Raman scattering process (ISRS) and a lower dephasing rate. Our results build on a foundation towards a deeper exploration of the coherent Raman response of two-dimensional materials.