Extended Higgs Sectors at Future $e^+ e^-$ Colliders

We compare several Beyond the Standard Model (SM) models with extended Higgs sec-tors. The models comprise the SM extended by a complex singlet field (CxSM), the 2-Higgs-Doublet Model with a CP-conserving (2HDM) and a CP-violating violating (C2HDM) scalarsector, the singlet extension of the 2- Higgs-Doublet Model (N2HDM), and the Next-to-Minimal Supersymmetric SM extension (NMSSM). All the above models have at least threeneutral bosons, with one being the 125 GeV Higgs boson. This common feature allows us tocompare the production and decay rates of the other two scalars. Using a set of benchmarkcentre-of-mass energies and luminosities, we discuss which models can be probed and if it ispossible to distinguish between them. Taking into account the expected accuracy in the mea-surements of the 125 GeV Higgs couplings, for the different CLIC configurations, we discusspossible deviations from its SM character, focusing on the CP-violating or the non-doubletcharacter of the 125 GeV Higgs boson. The expected precision at electron-positron colliderswill certainly contribute to a clearer picture of the nature of the Higgs boson