  If dark matter inhabits an expanded "hidden sector", annihilations may
proceed through sequential decays or multi-body final states. We map out the
potential signals and current constraints on such a framework in indirect
searches, using a model-independent setup based on multi-step hierarchical
cascade decays. While remaining agnostic to the details of the hidden sector
model, our framework captures the generic broadening of the spectrum of
secondary particles (photons, neutrinos, e+e- and antiprotons) relative to the
case of direct annihilation to Standard Model particles. We explore how
indirect constraints on dark matter annihilation limit the parameter space for
such cascade/multi-particle decays. We investigate limits from the cosmic
microwave background by Planck, the Fermi measurement of photons from the dwarf
galaxies, and positron data from AMS-02. The presence of a hidden sector can
change the constraints on the dark matter annihilation cross section by up to
an order of magnitude in either direction (although the effect can be much
smaller). We find that generally the bound from the Fermi dwarfs is most
constraining for annihilations to photon-rich final states, while AMS-02 is
most constraining for electron and muon final states; however in certain
instances the CMB bounds overtake both, due to their approximate independence
of the details of the hidden sector cascade. We provide the full set of cascade
spectra considered here as publicly available code with examples at
http://web.mit.edu/lns/research/CascadeSpectra.html.
