  A possibility of DM being multicomponent has a strong implication on
resolving decades-long known cosmological problems on small scale. In addition
to elastic scattering, the model allows for inelastic interactions, which can
be characterized by a 'velocity kick' parameter. The simplest 2cDM model with
cross section $0.01\lesssim\sigma/m<1\textrm{ cm}^{2}{ \rm g}^{-1}$ and the
kick velocity $V_{k}\simeq 100\textrm{ km s}^{-1}$ has been shown to robustly
resolve the missing satellites, core-cusp, and too-big-to-fail problems in
$N$-body cosmological simulations tested on MW-like haloes of a virial mass
$\sim5 \times 10^{11}$ M$_{\odot}$ (Paper I $\&$ II). With the aim of further
constraining the parameter space available for the 2cDM model, we extend our
analysis to dwarf and galaxy cluster haloes with their virial mass of $\sim
10^7 - 10^8$ and $\sim 10^{13} - 10^{14}$ M$_{\odot}$, respectively. We find
$\sigma_{0} / m \gtrsim 0.1 \textrm{ cm}^{2}{\rm g}^{-1}$ is preferentially
disfavored for both dwarfs and galaxy cluster haloes in comparison with
observations, while $\sigma_{0} / m = 0.001 \textrm{ cm}^{2}{\rm g}^{-1}$
causes little perceptible difference from that of the CDM counterpart for most
of the cross section's velocity dependence studied in this work. Our main
result is that within the reasonable set of parameters the 2cDM model can
successfully explain the observational trends seen in dwarf galaxy and galaxy
cluster haloes and the model leaves us an open window for other possible
alternative DM models.

Cosmology and Nongalactic Astrophysics