  Self-organized criticality elucidates the conditions under which physical and
biological systems tune themselves to the edge of a second-order phase
transition, with scale invariance. Motivated by the empirical observation of
bimodal distributions of activity in neuroscience and other fields, we propose
and analyze a theory for the self-organization to the point of
phase-coexistence in systems exhibiting a first-order phase transition. It
explains the emergence of regular avalanches with attributes of
scale-invariance which coexist with huge anomalous ones, with realizations in
many fields.
