A nonlinear plasmonic resonator design is proposed for three-state all-optical switching at frequencies including near infrared and lower red parts of the spectrum. The tri-stable response required for three-state operation is obtained by enhancing nonlinearities of a Kerr medium through multiple (higher order) plasmons excited on resonator’s metallic surfaces. Indeed, simulations demonstrate that exploitation of multiple plasmons equips the proposed resonator with a multi-band tri-stable response, which cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing.