Plasmonic devices have a unique ability to concentrate and convert optical energy into a small volume. There is a tremendous interest in achieving active control of plasmon resonances, which would enable switchable hotspots for applications such as surface-enhanced spectroscopy and single molecule emission. The small footprint and strong-field confinement of plasmonic nanoantennas also holds great potential for achieving transistor-type devices for nanoscale-integrated circuits. To achieve such a functionality, new methods for nonlinear modulation are required, which are able to precisely tune the nonlinear interactions between resonant antenna elements. Here we demonstrate that resonant pumping of a nonlinear medium in a plasmonic hotspot produces an efficient transfer of optical Kerr nonlinearity between different elements of a multifrequency antenna. By spatially and spectrally separating excitation and readout, isolation of the hotspot-mediated ultrafast Kerr nonlinearity from slower, thermal effects is achieved.