  We theoretically study coherent multiple Andreev reflections in a biased
three-terminal Josephson junction. We demonstrate that the direct current
flowing through the junction consists of supercurrent components when the bias
voltages are commensurate. This dissipationless current depends on the phase in
the superconducting leads and stems from the Cooper pair transfer processes
induced by non-local Andreev reflections of the quasiparticles originating from
the superconducting leads. We identify supercurrent-enhanced lines in the
current and conductance maps of the recent measurement [Y. Cohen, et al., PNAS
115, 6991 (2018)] on a nanowire Josephson junction and show that the magnitude
of the phase-dependent current components is proportional to the junction
transparency with the power corresponding to the component order.
