  Resonant excitation is an essential tool in the development of semiconductor
quantum dots (QDs) for quantum information processing. One central challenge is
to enable a transparent access to the QD signal without post-selection
information loss. A viable path is through cavity enhancement, which has
successfully lifted the resonantly scattered field strength over the laser
background under \emph{weak} excitation. Here, we extend this success to the
\emph{saturation} regime using a QD-micropillar device with a Purcell factor of
10.9 and an ultra-low background cavity reflectivity of just 0.0089. We achieve
a signal to background ratio of 50 and an overall system responsivity of 3~\%,
i.e., we detect on average 0.03 resonantly scattered single photons for every
incident laser photon. Raising the excitation to the few-photon level, the QD
response is brought into saturation where we observe the Mollow triplets as
well as the associated cascade single photon emissions, without resort to any
laser background rejection technique. Our work offers a new perspective toward
QD cavity interface that is not restricted by the laser background.
