  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 $M \sim 4-5 \times10^{11}
M_{\odot}$ 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.
