The intensity evolution of the Cu $K{\ensuremath{\beta}}_{1,3}$ and $K{\ensuremath{\beta}}_{2,5}$ emission spectra is measured as a function of excitation energy using resonant inelastic x-ray scattering spectroscopy. The contribution of $\underset{̱}{1s3d}$ shake satellites to the Cu $K{\ensuremath{\beta}}_{1,3}$ as well as to the Cu $K{\ensuremath{\beta}}_{2,5}$ emission spectrum is extracted. Both emission spectra indicate an additional contribution of $\underset{̱}{1s3p}$ shake satellites. The intensity evolution of the shake satellites from threshold to saturation is compared to the Thomas model and shows a similar saturation behavior as found for the Cu $K{\ensuremath{\alpha}}_{1,2}$ $\underset{̱}{1s3d}$ shake satellites, stating that the shake process is independent of the reemission shell. These $\underset{̱}{1s3d}$ shake satellites rapidly reach their saturation limit in contrast to Cu $\underset{̱}{1s2p}$ and $\underset{̱}{1s1s}$ shake satellites. Furthermore, the contribution of the $KMN$ and the $KNN$ radiative Auger satellites to the Cu $K{\ensuremath{\beta}}_{1,3}$ and Cu $K{\ensuremath{\beta}}_{2,5}$ emission spectra is obtained, respectively. The $KNN$ radiative Auger satellite is shown to play an important role in the interpretation of valence fluorescence spectra.