Crossed Andreev reflection (cAR) is a scattering process that happens in a quantum transport setup consisting of two normal metals (NM) attached to a superconductor (SC), where an electron incident from one NM results in a hole emerging in the other. Typically, electron tunneling (ET) through the superconductor from one NM to the other competes with cAR and masks its signature in the conductance spectrum. We propose a scheme to enhance cAR, in which the SC part of the NM-SC-NM is side coupled to another SC having a different superconducting phase to form a Josephson junction in the transverse direction. At strong enough coupling and for a large enough phase difference, one can smoothly traverse between the highly ET-dominant to the highly cAR-dominant transport regimes by tuning chemical potential, due to the appearance of subgap Andreev states that are extended in the longitudinal direction. We discuss connections to realistic systems.