Multi-component dark matter scenarios constitute natural extensions of standard single-component setups and offer attractive new dynamics that could be adopted to solve various puzzles of dark matter. In this work we present and illustrate properties of a minimal UV-complete vector-fermion dark matter model where two or three dark sector particles are stable. The model we consider is an extension of the Standard Model (SM) by spontaneously broken extra $U(1)_X$ gauge symmetry and a Dirac fermion. All terms in the Lagrangian which are consistent with the assumed symmetry are present, so the model is renormalizable and consistent. To generate mass for the dark-vector $X_mu$ the Higgs mechanism with a complex singlet $S$ is employed in the dark sector. Dark matter candidates are the massive vector boson $X_mu$ and two Majorana fermions $psi_pm$. All the dark sector fields are singlets under the SM gauge group. The set of three coupled Boltzmann equations has been solved numerically and discussed. We have performed scans over the parameter space of the model implementing the total relic abundance and direct detection constraints. The dynamics of the vector-fermion dark matter model is very rich and various interesting phenomena appear, in particular, when the standard annihilations of a given dark matter are suppressed then the semi-annihilations,
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