We discuss nonstandard interpretations of the 750 GeV diphoton excess recently reported by the ATLAS and CMS Collaborations which do not involve a new, relatively broad resonance with a mass near 750 GeV. Instead, we consider the sequential cascade decay of a much heavier, possibly quite narrow, resonance into two photons along with one or more additional particles. The resulting diphoton invariant mass signal is generically rather broad, as suggested by the data. We examine three specific event topologies-the "antler," the "sandwich," and the two-step cascade decay-and show that they all can provide a good fit to the observed published data. In each case, we delineate the preferred mass parameter space selected by the best fit. In spite of the presence of extra particles in the final state, the measured diphoton p_{T} spectrum is moderate due to its anticorrelation with the diphoton invariant mass. We comment on the future prospects of discriminating with higher statistics between our scenarios, as well as from more conventional interpretations.