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 nonlocal 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 [PNAS 115, 6991 (2018)10.1073/pnas.1800044115] 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.@en