  We present optimal control strategies for the DC transport across a Josephson
junction. Specifically, we consider a junction in which the Josephson coupling
is driven parametrically, with either a bichromatic or a trichromatic driving
protocol, and optimize the prefactor of the 1/$\omega$ divergence of the
imaginary part of the conductivity. We demonstrate that for an optimal
bichromatic protocol an enhancement of 70 can be reached, and for an optimal
trichromatic protocol an enhancement of 135. This is motivated by pump-probe
experiments that have demonstrated light-enhanced superconductivity along the
c-axis of underdoped YBCO, where the junction serves as a minimal model for the
c-axis coupling of superconducting layers. Therefore, the significant
enhancement of superconductivity that we show for multi-frequency protocols
demonstrates that the advancement of pump-probe technology towards these
strategies is highly desirable.
