Could the width of the diphoton anomaly signal a three-body decay?

The recently observed diphoton anomaly at the LHC appears to suggest the presence of a rather broad resonance. In this note, it is pointed out that this broadness is not called for if the two photons are produced along with an extra state. Specifically, the diphoton invariant mass arising from various A→BγγA→Bγγ processes, with A,BA,B being scalars, fermions, or vectors, though peaked at a rather large value, would naturally be broad and could fit rather well the observed deviations. This interpretation has a number of advantages over the two-photon resonance hypothesis, for example with respect to the compatibility with the 8 TeV diphoton, dilepton or dijet searches, and opens many new routes for New Physics model construction.