  In the TeV scale minimal left-right symmetric model (LRSM) for neutrino
masses, there is a tension between the flavor changing Higgs effects which
prefer an $SU(2)_R$ breaking scale $v_R \gtrsim (15-25)$ TeV depending on
whether the theory is kept invariant under charge conjugation ($Q_L\to
(Q_R)^c$) or under parity ($Q_L\to Q_R$) respectively and an LHC accessible
few-TeV range mass of $W_R$ boson which would require $v_R \lesssim 10 \, (15)$
TeV if $g_R/g_L = 1 (0.65)$. This requires one quartic coupling in the scalar
potential to go non-perturbative, posing a theoretical problem if the $W_R$ is
discovered at LHC. We propose a simple extension of the minimal LRSM that adds
a $B-L=0$ scalar triplet and study how this can ameliorate this tension. We
find that such a model is also constrained from various considerations and
implies a lower bound on the $W_R$ mass of 8.1 (5.26) TeV for the parity case
with $g_R/g_L= 1\, (0.65)$ and 4.85 (3.16) TeV for the case of charge
conjugation, if the flavor constraints have to be avoided while keeping all
couplings perturbative. These mass ranges are accessible at the high-luminosity
LHC. The model also implies new decay mode of $W_R$ to two scalars which is
absent in the minimal LRSM. Finally we comment on the impact of such a scalar
multiplet for a class of dark matter extension of LRSM discussed in the
literature recently.
