  We present the CP-violating Next-to-2-Higgs-Doublet Model (CN2HDM) which is
based on the extension of the CP-violating 2-Higgs-Doublet-Model (C2HDM) by a
complex singlet field that obeys a discrete $\mathbb{Z}_2$ symmetry. The model
thus features not only CP violation required for successful electroweak
baryogenesis but also a Dark Matter (DM) candidate. The model has an extended
Higgs sector with four CP-mixing visible neutral Higgs bosons, a DM candidate
and a pair of oppositely charged Higgs bosons. The possibility of singlet and
CP-odd admixtures to the observed Higgs boson in addition to the large number
of visible scalar particles leads to an interesting Higgs phenomenology. We
find that the model can easily provide 100\% of the DM relic density and
investigate interesting LHC and DM observables within the model. We provide all
the tools necessary to study the CN2HDM in detail and point out future research
directions for this interesting benchmark model that can address some of the
most pressing open questions of the Standard Model.
