  The confirmation of the Higgs boson in Run I data at the Large Hadron
Collider (LHC) and the excesses in recent Run II data suggest scenarios beyond
the Standard Model (SM). We pursue a study in a minimal model which is an
extension of a scalar doublet in the SM known as two-Higgs doublet model
(THDM). Following earlier suggestions two real scalars $\chi$ and $S$ have been
introduced in the THDM where $\chi$ is treated as a candidate for dark matter.
$\chi$ does not receive any vacuum expectation value ($vev$) in the model
whereas the Higgs-like scalar $S$ acquires $vev$. This allows small mixing
between the $CP$-even scalars of the THDM, $h$, $H$ and $S$. In this study the
mass spectrum of new scalars is taken to be $2 m_h < m_H < 2 m_t$, $m_\chi <
m_h/2$, $m_h \lesssim m_S \lesssim m_H - m_h$, $m_A > 2 m_t$ and $m_H^\pm <
m_A$, where $m_h$ and $m_t$ is masses of the SM Higgs and top-quark
respectively, $m_H, m_A$ and $m_{H^\pm}$ are the masses of the heavy $CP$-even
scalar $H$, $CP$-odd scalar $A$, and charged Higgs $H^\pm$, respectively. A
partial list of potential search channels at the LHC has been provided with
possible phenomenological consequences. The expected phenomenology and
constraints on parameters are also discussed in a model-independent approach .
