The phenomenology of several Beyond the Standard Model (SM) extensions that include extended Higgs sectors will be presented. The models discussed are: the SM extended by a complex singlet field (CxSM), the 2-Higgs-Doublet Model with a CP-conserving (2HDM) and a CP-violating (C2HDM) scalar sector, 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 three neutral scalars, with one being the 125 GeV Higgs boson. This common feature allows us to compare the production and decay rates of the other two scalars and therefore to compare their behaviour at future electron-positron colliders. Using predictions on the expected precision of the 125 GeV Higgs boson couplings at these colliders we are able to obtain the allowed admixtures of either a singlet or a pseudoscalar to the observed 125 GeV scalar, how much CP-violating can the Yukawa couplings have, among other. Therefore, even if no new scalar is found, the expected precision at future electron-positron colliders, such as CLIC, will certainly contribute to a clearer picture of the nature of the discovered Higgs boson.