Heterostructures combining two or more metal and/or semiconductor nanoparticles exhibit enhanced upconversion arising from localized nanoparticle resonances. However, plasmon-exciton coupling in semiconductor-metal nanostructures exhibits nanosecond relaxation times, and multi-plasmon metallic heterostructures are not broadly tunable. Here, we develop a biplasmonic heterostructure in which CuS and Au nanoparticle layers, separated by an alumina spacer of variable thickness, exhibit enhanced second- and third-harmonic generation due to dipole-dipole coupling between Au and CuS plasmons, as seen in the characteristic inverse sixth-power dependence of their separation in the measured harmonic enhancement and confirmed by numerical simulations of near-field CuS-Au nanoparticle coupling. Transient-absorption spectroscopy shows faster relaxation in Au/CuS (690 femtoseconds) compared to CuS heterostructures (929 femtoseconds). Moreover, nonlinear absorption measurements provide evidence for harmonic-induced plasmonic resonant energy transfer between the narrow Au and broad, tunable CuS plasmon resonances. This prototype for ultrafast upconversion showcases a strategy for high-efficiency, tunable plasmonic nonlinear devices with promising applications in photocatalysis, parametric down-conversion, and biomedical imaging.