  Dissipative dark matter arising from a hidden sector consisting of $N_{\rm
sec}$ exact copies of the Standard Model is discussed. The particles from each
sector interact with those from the other sectors by gravity and via the
kinetic mixing interaction, described by the dimensionless parameter,
$\epsilon$. It has been known for some time that models of this kind are
consistent with large scale structure and the cosmic microwave background
measurements. Here, we argue that such models can potentially explain various
observations on small scales, including the observed paucity and planar
distribution of satellite galaxies, the flat velocity function of field
galaxies, and the structure of galaxy halos. The value of the kinetic mixing
parameter is estimated to be $\epsilon \approx 1.2 \times 10^{-10}$ for $N_{\rm
sec} = 5$, the example studied in most detail here. We also comment on cluster
constraints such as those which arise from the Bullet cluster.
