  If dark matter is embedded in a non-trivial dark sector, it may annihilate
and decay to lighter dark-sector states which subsequently decay to the
Standard Model. Such scenarios - with annihilation followed by cascading
dark-sector decays - can explain the apparent excess GeV gamma-rays identified
in the central Milky Way, while evading bounds from dark matter direct
detection experiments. Each 'step' in the cascade will modify the observable
signatures of dark matter annihilation and decay, shifting the resulting
photons and other final state particles to lower energies and broadening their
spectra. We explore, in a model-independent way, the effect of multi-step
dark-sector cascades on the preferred regions of parameter space to explain the
GeV excess. We find that the broadening effects of multi-step cascades can
admit final states dominated by particles that would usually produce too
sharply peaked photon spectra; in general, if the cascades are hierarchical
(each particle decays to substantially lighter particles), the preferred mass
range for the dark matter is in all cases 20-150 GeV. Decay chains that have
nearly-degenerate steps, where the products are close to half the mass of the
progenitor, can admit much higher DM masses. We map out the region of
mass/cross-section parameter space where cascades (degenerate, hierarchical or
a combination) can fit the signal, for a range of final states. In the current
work, we study multi-step cascades in the context of explaining the GeV excess,
but many aspects of our results are general and can be extended to other
applications.
