  We consider a model of two-component dark matter based on a hidden $U(1)_D$
symmetry, in which relic densities of the dark matter are determined by
forbidden channels and thermal freeze-out. The hidden $U(1)_D$ symmetry is
spontaneously broken to a residual $\mathbb{Z}_4$ symmetry, and the lightest
$\mathbb{Z}_4$ charged particle can be a dark matter candidate. Moreover,
depending on the mass hierarchy in the dark sector, we have two-component dark
matter. We show that the relic density of the lighter dark matter component can
be determined by forbidden annihilation channels which require larger couplings
compared to the normal freeze-out mechanism. As a result, a large
self-interaction of the lighter dark matter component can be induced, which may
solve small scale problems of $\Lambda$CDM model. On the other hand, the
heavier dark matter component is produced by normal freeze-out mechanism. We
find that interesting implications emerge between the two dark matter
components in this framework. We explore detectabilities of these dark matter
particles and show some parameter space can be tested by the SHiP experiment.
