  We consider an extension of the Standard Model that accounts for the muon
$g-2$ tension and neutrino masses and study in detail dark matter
phenomenology. The model under consideration includes a WIMP and a FIMP scalar
dark matter candidates and thus gives rise to two-component dark matter
scenarios. We discuss different regimes and mechanisms of production, including
the novel freeze-in semi-production, and show that the WIMP and FIMP together
compose the observed relic density today. The presence of the extra scalar
fields allows phase transitions of the first order. We examine the evolution of
the vacuum state and discuss stochastic gravitational wave signals associated
with the first-order phase transition. We show that the gravitational wave
signals may be probed by future gravitational wave experiments which may serve
as a complementary detection signal.
