We study the impact of double-and triple-scattering contributions on coherent backscattering of laser light from saturated isotropic atoms in the helicity-preserving polarization channel. By using the recently proposed diagrammatic pump-probe approach, we analytically derive single-atom spectral responses to a classical polychromatic driving field, combine them self-consistently to double-and triple-scattering processes, and numerically deduce the corresponding elastic and inelastic spectra, as well as the total backscattered intensities. We find that accounting for the triple-scattering contribution leads to a faster decay of phase-coherence with increasing saturation of the atomic transition as compared with double scattering alone and to a better agreement with the experiment on strontium atoms.