I will briefly review the shortcomings of the 2HDMs in terms of providing a new source of CP violation (desired for baryogenesis), as well as a Dark Matter candidate, before discussing how this is achieved with three doublets. In the realm of three doublets, we need to impose some symmetry, in order to retain some predictivity. I will illustrate this with three examples.
With support from FCT through project UIDB/00777/2020
