The CDF collaboration recently reported a measurement of the W -boson mass M W whose value shows a large upward deviation from the Standard Model (SM) prediction. The question arises whether such large values of  M W could be accommodated in extensions of the SM without violating other constraints and which phenomenological consequences this would have. A different type of deviation from the SM has been observed experimentally in the searches for light Higgs bosons. CMS has observed two excesses with a local significance of about 3 σ in the γ γ and τ + τ - final states for a hypothetical Higgs-boson mass of approximately 95 GeV. These two excesses are compatible with the corresponding ATLAS limits. Earlier an excess was also observed in the Higgs-boson searches at LEP in the b b ¯ final state at the local 2 σ confidence level at about the same mass. It was shown recently that the three excesses can be accommodated in a Two-Higgs-Doublet Model that is extended with a real singlet (N2HDM) of Yukawa type IV, while being in agreement with all other theoretical and experimental constraints. We demonstrate here that the region of the parameter space that describes the three excesses can also give rise to a large contribution to M W in agreement with the recent CDF measurement. We discuss further phenomenological consequences of this scenario.