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In this paper, we construct for the first time a two-component stronglyinteracting massive particles (SIMP) dark matter (DM) model, where a complexscalar and a vector-like fermion play the role of the SIMP DM candidates. Thesetwo particles are stable due to an accidental $\mathbb{Z}^{}_4$ symmetry afterthe breaking of a $\text{U}(1)^{}_\textsf{D}$ gauge symmetry. By introducingone extra complex scalar as a mediator between the SIMP particles, this modelcan have $3 \to 2$ processes that determine the DM relic density. On the otherhand, the SIMP DM particles can maintain kinetic equilibrium with the thermalbath 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 wouldredistribute the SIMP DM number densities after the chemical freeze-out of DM.Moreover, this redistribution would significantly modify the predictions of theself-interacting cross section of DM compared with other SIMP models. It iscrucial to include the two-loop induced $2 \to 2$ annihilations to obtain thecorrect DM phenomenology.

Scalar and Fermion Two-component SIMP Dark Matter with an Accidental $\mathbb{Z}^{}_4$ Symmetry