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We study the effect of non-standard neutrino interactions (NSIs) on the growth of instabilities in neutrino energy spectra of a core-collapse supernova for different neutrino intensities and/or types of NSIs, notably including the exotic neutrino magnetic moment. Although it is usually attested that instabilities virtually smear out all potentially observable signatures, we show there are regimes in which they work as a magnifying glass, bringing tiny effects to the eye of the observer.