Recent experiments demonstrate that plasmonic resonators can enhance the four-wave mixing (FWM) process by several orders of magnitude, due to the localization of the incident fields. We show that, when the plasmonic resonator is coupled to two quantum emitters, a three orders of magnitude enhancement can be obtained on top of the enhancement due to the localization. We explicitly demonstrate-on an expression for the steady-state FWM amplitude-how the presence of a Fano resonance leads to the cancellation of nonresonant terms in a FWM process. A cancellation in the denominator gives rise to an enhancement in the nonlinearity. The explicit demonstration we present here guides one to a method for achieving even larger enhancement factors by introducing additional coupling terms. The method is also applicable to Fano resonances induced by all-plasmonic couplings, which are easier to control in experiments.