  The CMS collaboration reported a $\sim 3 \, \sigma$ (local) excess at
$96\;$GeV in the search for light Higgs-boson decaying into two photons. This
mass coincides with a $\sim 2 \, \sigma$ (local) excess in the $b\bar b$ final
state at LEP. We show an interpretation of these possible signals as the
lightest Higgs boson in the 2 Higgs Doublet Model with an additional complex
Higgs singlet (2HDMS). The interpretation is in agreement with all experimental
and theoretical constraints. We concentrate on the 2HDMS type II, which
resembles the Higgs and Yukawa structure of the Next-to Minimal Supersymmetric
Standard Model. We discuss the experimental prospects for constraining our
explanation at future $e^+e^-$ colliders, with concrete analyses based on the
ILC prospects.
