In this paper we present a study of some relevant steps of the hierarchical frequency-Hough (FH) pipeline, used within the LIGO and Virgo Collaborations for wide-parameter space searches of continuous gravitational waves (CWs) emitted, for instance, by spinning neutron stars (NSs). Because of their weak expected amplitudes, CWs have not been still detected so far. These steps, namely the spectral estimation, the {\it peakmap} construction and the procedure to select candidates in the FH plane, are critical as they contribute to determine the final search sensitivity. Here, we are interested in investigating their behavior in the (presently quite) extreme case of signal clusters, due to many and strong CW sources, emitting gravitational waves (GWs) within a small (i.e.