  We investigate the effects of nonstandard four-fermion neutrino-neutrino
interactions on the flavor evolution of dense neutrino gases. We find that in
the regions where the neutrino-neutrino refractive index leads to collective
flavor oscillations, the presence of new neutrino interactions can produce
flavor equilibration in both normal and inverted neutrino mass hierarchy. In
realistic supernova environments, these effects are significant if the
nonstandard neutrino-neutrino interaction strength is comparable to the one
expected in the standard case, dominating the ordinary matter potential.
However, very small nonstandard neutrino-neutrino couplings are enough to
trigger the usual collective neutrino flavor transformations in the inverted
neutrino mass hierarchy, even if the mixing angle vanishes exactly.
