In this work, we derive and present the coupled amplitude equations to describe the evolutions of different spectral components in different transverse modes for Raman fiber amplifiers (RFAs). Both the effects of the four-wave-mixing in the fundamental mode (FM FWM) and the inter-modal four-wave-mixing (IM FWM) on high-power RFAs are demonstrated through numerical simulations. Specifically, effective FM FWM interaction could occur and lead to a drop of the 2nd order Raman limit for RFAs by over 50%, despite that the corresponding wave-vector mismatch is rather big. In addition, the IM FWM could also impact the 2nd order Raman limit for RFAs with additional generation of the first order Raman Stokes light in the higher-order mode. We also investigate the effects of the intensity fluctuations in the initial inserted pump and seed lasers on high-power RFAs. It reveals that the temporal stability of the initial inserted pump laser has much more significant impacts on high-power RFAs than that of the initial inserted seed laser. Notably, through applying temporal stable laser as the initial inserted pump laser, both the FM FWM and IM FWM effects could be effectively suppressed, and the 2nd order Raman limit for high-power RFAs could be increased by over twice.