  The new measurement of the $W$ boson mass performed by the CDF experiment at
the Tevatron shows a significant deviation not only with the expectation in the
Standard Model but also with other precision measurements performed at LEP, the
Tevatron and the LHC. We nevertheless take this new measurement at face value
and interpret it as an effect of new physics. We particularly try to link it
with other possible anomalies such as the recent muon $g-2$ and consider a
scenario that addresses some shortcomings of the Standard Model. We show that a
model with two doublets and a light pseudoscalar Higgs fields, supplemented by
a stable isosinglet fermion, can simultaneously explain the possible $M_W$ and
$(g-2)_\mu$ anomalies and accounts for the weakly interacting massive particle
that could be responsible of the dark matter in the universe.
