Raman fiber lasers, known for their capacity to provide both high-power and precise wavelength emissions, are gaining attraction across a spectrum of applications, including fiber optic communications, sensing, spectroscopy, and imaging. However, the scalability of Raman laser power is impeded by the constraints of pump brightness and the deleterious effects of second-order Raman scattering. In this research, we have undertaken a comprehensive experimental and simulation-based investigation into the impact of pump brightness on the output characteristics within an amplifier framework. Our innovative approach integrates high-brightness pumping with multi-mode graded index fibers. Notably, we have pioneered the introduction of multi-wavelength seed light to facilitate four-wave mixing, thereby effectively mitigating higher-order Raman scattering. This novel strategy has culminated in the achievement of a 4 kW Raman laser output in an all-fiber configuration, representing the highest output power reported so far.