The interaction of intense laser pulses with size-selected F(-)(NF3)n clusters is experimentally studied. Intense-field double- and multiple-detachment processes in the isolated atomic F(-) anion and in electrostatically bound F(-)(NF3) dimer and F(-)(NF3)2 trimer systems are directly compared. Both dimer and trimer systems are found to exhibit similar enhancement of the highly nonlinear processes, with respect to the atomic system, as reflected in significantly lower saturation intensities. The dependencies of different product channels as a function of laser peak intensity, polarization ellipticity, and laser pulse shape are presented, indicating an efficient nonrescattering mechanism.