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 theoretical and experimental constraints from dark matter, flavour physics and collider searches. Further, we discuss a few benchmark scenarios to test the discovery potential for the 2HDMS at the HL-LHC and at future high-energy e+e− colliders.