  Recent investigations on optical nonlinearities of plasmonic materials
suggest their responses may be even beyond the usual perturbative description.
To better understand these surprisingly strong responses, we develop here a
simple but general approach to describe the nonlinear optical response of
plasmonic materials up to $n$th perturbation order. We apply the approach to
understand spectral broadening occurring in resonant metasurfaces and
investigate the enhancement of high-harmonic generation from multiply-resonant
metasurfaces, predicting an over million-fold enhancement of higher harmonics.
