The multicomponent dark matter model with self-scattering and inter-conversions of species into one another is an alternative dark matter paradigm that is capable of resolving the long-standing problems of \Lambda CDM cosmology at small scales . In this paper , we have studied in detail the properties of dark matter halos with M \sim 4 - 5 \times 10 ^ { 11 } M _ { \odot } obtained in N -body cosmological simulations with the simplest two-component ( 2cDM ) model . A large set of velocity-dependent cross-section prescriptions for elastic scattering and mass conversions , \sigma _ { s } ( v ) \propto v ^ { a _ { s } } and \sigma _ { c } ( v ) \propto v ^ { a _ { c } } , has been explored and the results were compared with observational data . The results demonstrate that self-interactions with the cross-section per particle mass evaluated at v = 100 km s ^ { -1 } being in the range of 0.01 \lesssim \sigma _ { 0 } / m \lesssim 1 cm ^ { 2 } g ^ { -1 } robustly suppress central cusps , thus resolving the core-cusp problem . The core radii are controlled by the values of \sigma _ { 0 } / m and the DM cross-section ’ s velocity-dependent power-law indices ( a _ { s } ,a _ { c } ) , but are largely insensitive to the species ’ mass degeneracy . These values are in full agreement with those resolving the substructure and too-big-to-fail problems . We have also studied the evolution of halos in the 2cDM model with cosmic time .