Generation of a broadband spectrum through various nonlinear effects, such as Raman scattering and intermodal four-wave mixing (IMFWM) in multimode fibers (MMFs), has emerged as a suitable cost-effective alternative to the existing highly nonlinear photonic crystal fiber-based systems. However, the application of such standard telecom-grade MMFs for continuum generation is limited by the large amount of power required to trigger and maintain the effect of such nonlinearities in them. Here, we experimentally demonstrate an all-fiber-based cascaded system comprising a standard multimode graded-index (GRIN) fiber and a few-mode non-zero dispersion-shifted (NZDS) fiber, which effectively reduces the Raman threshold. The proposed cascaded fiber system is pumped by a passively Q-switched 770 ps Nd:YAG laser operating at 1064 nm, utilizing the normal dispersion regime of both fibers. Cascaded Raman scattering up to the fourth order and IMFWM processes were observed at a comparatively low average input pump power of 6 mW (corresponding peak power of similar to 339 W), making our system more efficient than the previous findings. The experimental observations are also verified with the theoretical estimations of the IMFWM-generated sidebands. Such a cascaded fiber system is highly suitable for low-power broadband tunable light sources in the telecom band.