  In this paper, we construct for the first time a two-component strongly
interacting massive particles (SIMP) dark matter (DM) model, where a complex
scalar and a vector-like fermion play the role of the SIMP DM candidates. These
two particles are stable due to an accidental $\mathbb{Z}^{}_4$ symmetry after
the breaking of a $\text{U}(1)^{}_\textsf{D}$ gauge symmetry. By introducing
one extra complex scalar as a mediator between the SIMP particles, this model
can have $3 \to 2$ processes that determine the DM relic density. On the other
hand, the SIMP DM particles can maintain kinetic equilibrium with the thermal
bath until the DM freeze-out temperature via the $\text{U}(1)^{}_\textsf{D}$
gauge couplings. Most importantly, we find an unavoidable two-loop induced $2
\to 2$ process tightly connecting to the $3 \to 2$ process that would
redistribute the SIMP DM number densities after the chemical freeze-out of DM.
Moreover, this redistribution would significantly modify the predictions of the
self-interacting cross section of DM compared with other SIMP models. It is
crucial to include the two-loop induced $2 \to 2$ annihilations to obtain the
correct DM phenomenology.
