Multi-component dark matter scenarios are studied in the model with $U(1)_X$ dark gauge symmetry that is broken into its product subgroup $Z_2 times Z_3$ {a} la Krauss-Wilczek mechanism. In this setup, there exist two types of dark matter fields, $X$ and $Y$, distinguished by different $Z_2 times Z_3$ charges. The real and imaginary parts of the $Z_2$-charged field, $X_R$ and $X_I$, get different masses from the $U(1)_X$ symmetry breaking. The field $Y$, which is another dark matter candidate due to the unbroken $Z_3$ symmetry, belongs to the Strongly Interacting Massive Particle (SIMP)-type dark matter. Both $X_I$ and $X_R$ may contribute to $Y$s $3rightarrow 2$ annihilation processes, opening a new class of SIMP models with a local dark gauge symmetry. Depending on the mass difference between $X_I$ and $X_R$, we have either two-component or three-component dark matter scenarios. In particular two- or three-component SIMP scenarios can be realised not only for small mass difference between $X$ and $Y$, but also for large mass hierarchy between them, which is a new and unique feature of the present model. We consider both theoretical and experimental constraints, and present four case studies of the multi-component dark matter scenarios.
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