  Recently it was shown that dark matter with mass of order the weak scale can
be charged under a new long-range force, decoupled from the Standard Model,
with only weak constraints from early Universe cosmology. Here we consider the
implications of an additional charged particle $C$ that is light enough to lead
to significant dissipative dynamics on galactic times scales. We highlight
several novel features of this model, which can be relevant even when the $C$
particle constitutes only a small fraction of the number density (and energy
density). We assume a small asymmetric abundance of the $C$ particle whose
charge is compensated by a heavy $X$ particle so that the relic abundance of
dark matter consists mostly of symmetric $X$ and $\bar{X}$, with a small
asymmetric component made up of $X$ and $C$. As the universe cools, it
undergoes asymmetric recombination binding the free $C$s into $(XC)$ dark atoms
efficiently. Even with a tiny asymmetric component, the presence of $C$
particles catalyzes tight coupling between the heavy dark matter $X$ and the
dark photon plasma that can lead to a significant suppression of the matter
power spectrum on small scales and lead to some of the strongest bounds on such
dark matter theories. We find a viable parameter space where structure
formation constraints are satisfied and significant dissipative dynamics can
occur in galactic haloes but show a large region is excluded. Our model shows
that subdominant components in the dark sector can dramatically affect
structure formation.
