  The Two Higgs Doublet model augmented with a complex scalar singlet (2HDMS)
is a well-motivated candidate for Beyond Standard Model (BSM) Physics. We
investigate the dark matter phenomenology of the 2HDMS with the complex scalar
singlet as the dark matter candidate. We perform a study of the parameter space
allowed by existing experimental constraints from dark matter, flavour physics
and collider searches. The distinction between real and complex scalar dark
matter in the context of the 2HDMS is also performed. Furthermore, we discuss
the discovery potential for the 2HDMS at the HL-LHC and at future high-energy
$e^+e^-$ colliders.
