  Self-Interacting Dark Matter models can successfully explain dark matter (DM)
production through interactions confined within the dark sector. However, they
often lack measurable experimental signals due to their secluded nature.
Including a feeble interaction with the visible sector through a Higgs portal
leads not only to potential detection avenues and richer thermal production
dynamics, but also to a possible explanation of the initial dark sector
population through the freeze-in mechanism. In this work we study, by solving
the full system of coupled Boltzmann equations for the number densities and
temperatures of all the involved states, three scenarios of this type where the
DM is: a real scalar with broken $\mathbb{Z}_2$, a complex scalar with unbroken
$\mathbb{Z}_3$, and a $\mathbb{Z}_3$ scalar with an additional scalar mediator.
All of these models have viable dark matter candidates in a cannibal phase
while having different detection profiles. We show that cosmological bounds can
be either exacerbated or evaded by changing the dark sector interactions,
leading to potential signatures in long-lived particle and indirect detection
experiments.
