The THDMa and possible $e^+e^-$ signatures

I here discuss the THDMa, a type II two Higgs doublet model that is enhanced by an additional pseudoscalar which serves as a portal to the dark matter sector containing a fermionic dark matter andidate. I present a recent scan of the models parameter space where all parameters are allowed to float freely, and discuss prospects for this model at future $e^+e^-$ colliders for cases that are not covered in standard THDM searches.