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It is possible to ameliorate the Higgs vacuum stability problem by switchingover to two Higgs doublet models (2HDM), ensuring a stable electroweak vacuumup to the Planck scale, even though the top quark mass may be on the high side.However, the simultaneous requirements of perturbative unitarity, and alsocompatibility with collider and flavour data, constrain the parameter spaceseverely. We investigate the collider signals answering to the regions allowedby such constraints. In particular, the near degeneracy of the neutral heavyscalar and the pseudoscalar is a feature that is probed. The LHC allowsdistinguishability of these two states, together with signal significance of atleast 3$\sigma$, in its high-luminosity run. While $e^+ e^-$ colliders may haverather low event rates, muon colliders, cashing on the principle of radiativereturn, can probe 2HDM scenarios with (pseudo)scalar masses up to a TeV or so,though with the price of losing distinction between the CP-even and odd states.

High-scale validity of a two Higgs doublet scenario: predicting collider signals