  We examine the possible indirect signatures of dark matter annihilation
processes with a non-standard scaling with the dark matter density, and in
particular the case where more than two dark matter particles participate in
the annihilation process. We point out that such processes can be strongly
enhanced at low velocities without violating unitarity, similar to Sommerfeld
enhancement in the standard case of two-body annihilation, potentially leading
to visible signals in indirect searches. We study in detail the impact of such
multi-body annihilations on the ionization history of the universe and
consequently the cosmic microwave background, and find that unlike in the
two-body case, the dominant signal can naturally arise from the end of the
cosmic dark ages, after the onset of structure formation. We examine the
complementary constraints from the Galactic Center, Galactic halo, and galaxy
clusters, and outline the circumstances under which each search would give rise
to the strongest constraints. We also show that if there is a population of
ultra-compact dense dark matter clumps present in the Milky Way with
sufficiently steep density profile, then it might be possible to detect point
sources illuminated by multi-body annihilation, even if there is no large
low-velocity enhancement. Finally, we provide a case study of a model where
3-body annihilation dominates the freezeout process, and in particular the
resonant regime where a large low-velocity enhancement is naturally generated.
