Here we extend the reach of Fano resonant coupling by combining this concept with cloaking and plasmonic resonances in a single nonlinear nanoparticle, in order to realize giant all-optical scattering nanoswitches controlled by moderate pumping intensities. We show that a core-shell nonlinear plasmonic particle may be designed to abruptly switch from being completely cloaked to being strongly resonant, with up to a 40 dB cross-sectional difference. Self-tunable optical cloaks and resonant scatterers are envisioned for use as efficient all-optical switches and nanomemories.