  While Anderson is a single-particle wave effect, guaranteeing a single
excitation in the system can be challenging. We here tackle this limitation in
the context of light localization in three dimensions in disordered cold atom
clouds, in presence of several photons. We show that the presence of these
multiple excitations does not affect substantially the abnormal intensity
fluctuations which characterize the Anderson localization transition, provided
that the radiated light is frequency filtered. Due to their narrow linewidth,
long-lived modes, and particularly the localized ones, are strongly saturated
even for a weak resonant pump, leading to a large increase of the inelastic
scattering and to reduced fluctuations in the total radiation. Yet the atomic
coherences and the resulting elastic scattering remain a proper witness of the
Anderson localization transition. Hence, frequency filtering allows one to
investigate the single-excitation sector, dismissing the many-body effects
showing up in the fluorescence spectrum.
