Raman backscattering (RBS) in plasma is the basis of plasma-based amplifiers and is important in laser-driven fusion experiments. Using theoretical model and particle-in-cell simulations, we show that saturation can arise from nonlinearities due to coupling between the fundamental and harmonic plasma wave modes for sufficiently intense pump and seed pulses. We present a time-dependent analysis that shows that plasma wave phase shifts reach a maximum close to wavebreaking. The study contributes to a new understanding of RBS saturation for counter-propagating laser pulses. More information on the dataset structure can be found in the README file.