The synthesis of adjacent overlapped Stokes spectra in two stages of a transient stimulated Raman chirped-pulse amplifier, tuned respectively to the vibrational modes at 901 and 767 cm−1 of a potassium gadolinium tungstate [KGd(WO4)2] crystal, is demonstrated. The contribution of the spatio-temporal overlap of seed and pump pulses, as well as the self-phase modulation, was investigated. The noncollinear configuration allows the composite bandwidth at the central wavelength of 1120 nm to be increased by a factor of 23 compared to the pump pulse bandwidth of 1.6 nm. After reaching a conversion efficiency of 35% in the second stage, the compressibility of a chirped Stokes pulse with a tailored spectrum was also investigated.