  We study the effect of interference on the lepton number violating~(LNV) and
lepton number conserving~(LNC) three-body meson decays $M_1^{+}\to l_i^{+}
l_j^{\pm}\pi^{\mp}$, that arise in a TeV scale Left Right Symmetric
model~(LRSM) with degenerate or nearly degenerate right handed~(RH) neutrinos.
LRSM contains three RH neutrinos and a RH gauge boson. The RH neutrinos with
masses in the range of $M_N \sim$ (MeV - few GeV) can give resonant enhancement
in the semi-leptonic LNV and LNC meson decays. In the case, where only one RH
neutrino contributes to these decays, the predicted new physics branching ratio
of semi-leptonic LNV and LNC meson decays $M_1^{+}\to l_i^{+} l_j^{+}\pi^{-}$
and $M_1^{+}\to l_i^{+} l_j^{-}\pi^{+}$ are equal. We find that with at least
two RH neutrinos contributing to the process, the LNV and LNC decay rates can
differ. Depending on the neutrino mixing angles and $CP$ violating phases, the
branching ratios of LNV and LNC decay channels mediated by the heavy neutrinos
can be either enhanced or suppressed, and the ratio of these two rates can
differ from unity.
