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In this paper, we studied the ``hyperon puzzle", a problem that nevertheless the large number of studies is still an open problem. The solution of this issue requires one or more mechanisms that could eventually provide the additional repulsion needed to make the EoS stiffer and, therefore, the value of $M_{\rm{max}, T}$ compatible with the current observational limits. In this paper we proposed that including dark matter (DM) admixed with ordinary matter in neutron stars (NSs), change the hydrostatic equilibrium and may explain the observed discrepancies, regardless to hyperon multi-body interactions, which seem to be unavoidable. We have studied how non-self-annihilating, and self-interacting, DM admixed with ordinary matter in NSs changes their inner structure, and discussed the mass-radius relations of such NSs. We considered DM particle masses of 1, 10, and 100 GeV, while taking into account a rich list of the DM interacting strengths, $y$. By analyzing the multidimensional parameter space, including several quantities like: a. the DM interacting strength, b. the DM particle mass as well as the quantity of DM in its interior, and c. the DM fraction, ${\rm f}_{DM}$, we put constraints in the parameter space ${\rm f}_{DM} - p^{\prime}_{\rm DM}/p^{\prime}_{\rm OM}$. Our bounds are sensitive to the recently observed NSs total masses.