  Resonance trapping appears in open many-particle quantum systems at high
level density when the coupling to the continuum of decay channels reaches a
critical strength. Here a reorganization of the system takes place and a
separation of different time scales appears. We investigate it under the
influence of additional weakly coupled channels as well as by taking into
account the real part of the coupling term between system and continuum. We
observe a saturation of the mean width of the trapped states. Also the decay
rates saturate as a function of the coupling strength. The mechanism of the
saturation is studied in detail. In any case, the critical region of
reorganization is enlarged. When the transmission coefficients for the
different channels are different, the width distribution is broadened as
compared to a chi_K^2 distribution where K is the number of channels. Resonance
trapping takes place before the broad state overlaps regions beyond the
extension of the spectrum of the closed system.
