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In the recently discovered heavy fermion superconductor CeRh2As2, a magnetic field induced phase transition has been observed inside the superconducting state, which is proposed to be a transition from an even to an odd-parity superconducting state. The odd-parity superconducting state and its large upper critical field has been explained by local inversion symmetry breaking and consequent Rashba spin-orbit coupling. Here we report the experimental tuning of the parity of superconductivity in CeRh2As2 via applied pressure. Superconductivity is enhanced by pressure after its initial suppression, forming a second dome. However, the odd-parity state only exists in the first dome and the second dome is dominated by the even-parity state. This parity switch of superconductivity under pressure is consistent with the competition between Rashba spin-orbit coupling and interlayer hopping in determining the parity of superconductivity in systems with local inversion symmetry breaking. Our results provide insightful guidance on how to look for new odd-parity superconductors.