Can black holes preserve $N > 4$ supersymmetry?

The dynamics of near-BPS black holes are governed by the breaking of the conformal symmetry that emerges near their horizons. Using the classification of superconformal symmetries, we systematically classify and quantize all effective theories that can arise in the near-BPS limit of black holes. Using these results, we argue, under certain physical assumptions, that BPS black holes cannot preserve more than four supercharges. This conclusion is consistent with existing constructions in string theory.