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.

24 pages + appendices, 7 figures. v2: references added, updated figures, matches published version