  A second Higgs doublet arises naturally as a parity partner of the standard
model (SM) Higgs, once SM is extended to its left-right symmetric version
(LRSM) to understand the origin of parity violation in weak interactions as
well as to accommodate small neutrino masses via the seesaw mechanism. The
flavor changing neutral Higgs (FCNH) effects in the minimal version of this
model (LRSM), however, push the second Higgs mass to more than 15 TeV making it
inaccessible at the LHC. Furthermore since the second Higgs mass is directly
linked to the $W_R$ mass, discovery of a "low" mass $W_R$ ($M_{W_R}\leq 5-6$
TeV) at the LHC would require values for some Higgs self couplings larger than
one. In this paper we present an extension of LRSM by adding a vector-like
$SU(2)_R$ quark doublet which weakens the FCNH constraints allowing the second
Higgs mass to be near or below TeV and a third neutral Higgs below 3 TeV for a
$W_R$ mass below 5 TeV. It is then possible to search for these heavier Higgs
bosons at the LHC, without conflicting with FCNH constraints. A right handed
$W_R$ mass in the few TeV range is quite natural in this class of models
without having to resort to large scalar coupling parameters. The CKM mixings
are intimately linked to the vector-like quark mixings with the known quarks,
which is the main reason why the constraints on the second Higgs mass is
relaxed. We present a detailed theoretical and phenomenological analysis of
this extended LR model and point out some tests as well as its potential for
discovery of a second Higgs at the LHC. Two additional features of the model
are: (i) a 5/3 charged quark and (ii) a fermionic top partner with masses in
the TeV range.
