  We propose a simple model of dark matter and CP violation and consider the
associated triple and quadruple productions of 125 GeV Higgs bosons at the
Large Hadron Collider (LHC). In the model, the dark matter is a vector-like
dark fermion $(\bar{\chi}, \chi)$ interacting with the Standard Model only
through a complex messenger scalar $S$ which is an electroweak singlet. New
sources of CP violation reside in the most general scalar potential involving
the doublet $H$ and the singlet $S$, as well as in the dark Yukawa coupling
between $S$ and $(\bar{\chi}, \chi)$. We study current experimental constraints
from Higgs measurements, searches for new scalars at the LHC, precision
electroweak measurements, EDM measurements, dark matter relic density, as well
as direct and indirect detections of dark matter. A smoking-gun signature of CP
violation could come from the Higgs-to-Higgs decays, $h_3\to h_2h_1$, where
$h_3/h_2/h_1$ are the heaviest scalar, second heaviest scalar and the SM-like
125-GeV Higgs, respectively. Taking into account other Higgs-to-Higgs decays,
such as $h_3\to 2h_2$ and $h_3/h_2\to 2h_1$, then gives rise to novel $3h_1$
and $4h_1$ final states, which have yet to be searched for experimentally. We
present four benchmarks and show the event rates for $3h_1$ and $4h_1$ final
states could be as large as ${\cal O}(10)\ {\rm fb}$ and ${\cal O}(1)\ {\rm
fb}$, respectively, at the 14-TeV LHC. This work opens up a new frontier of
searching for triple and quadruple Higgs bosons at a high energy collider.
