The conservation of lepton flavor and total lepton number are no longer guaranteed in the Standard Model after the discovery of neutrino oscillations. µ − + N (A, Z) → e + + N (A, Z − 2) conversion in a muonic atom is one of the most promising channels to investigate the lepton number violation processes, and measurement of the µ − − e + conversion is planned in future µ − − e − conversion experiments with a muonic atom in a muon-stopping target. This letter discusses experimental strategies to maximize the sensitivity of the µ − − e + conversion experiment by introducing the new requirement of the mass relation of M (A, Z − 2) < M (A, Z − 1), where M (A, Z) is the mass of the muon-stopping target nucleus, to eliminate the backgrounds from radiative muon capture. The sensitivity of the µ − − e + conversion is expected to be improved by four orders of magnitude in forthcoming experiments using a proper target nucleus that satisfies the mass relation. The most promising isotopes found are 40 Ca and 32 S.