  Plasmonic nanostructures enhance nonlinear response, such as surface enhanced
Raman scattering (SERS), by localizing the incident field into hot spots. The
localized hot spot field can be enhanced even further when linear Fano
resonances (FR) take place in a double resonance scheme. However, hot spot
enhancement is limited with the modification of the vibrational modes, the
break-down of the molecule and the tunnelling regime. Here, we present a method
which can circumvent these limitations. Our analytical model and solutions of
3D Maxwell equations show that: enhancement due to the localized field can be
multiplied by a factor of $10^2$ to $10^3$. Moreover, this can be performed
without increasing the hot spot intensity which also avoids the modification of
the Raman modes. Unlike linear Fano resonances, we create a path interference
in the nonlinear response. We demonstrate on a single equation that enhancement
takes place due to cancellation of the contributing terms in the denominator of
the SERS response.
