  We put forth a mechanism for enhancing the interlayer transport in cuprate
superconductors, by optically driving plasmonic excitations along the $c$ axis
with a frequency that is blue-detuned from the Higgs frequency. The plasmonic
excitations induce a collective oscillation of the Higgs field which induces a
parametric enhancement of the superconducting response, as we demonstrate with
a minimal analytical model. Furthermore, we perform simulations of a
particle-hole symmetric $U(1)$ lattice gauge theory and find good agreement
with our analytical prediction. We map out the renormalization of the
interlayer coupling as a function of the parameters of the optical field and
demonstrate that the Higgs mode mediated enhancement can be larger than $50\%$.
