  We prove that the only asymptotically flat spacetimes with a suitably regular
event horizon, in a generalised Majumdar-Papapetrou class of solutions to
higher-dimensional Einstein-Maxwell theory, are the standard multi-black holes.
The proof involves a careful analysis of the near-horizon geometry and an
extension of the positive mass theorem to Riemannian manifolds with conical
singularities. This completes the classification of asymptotically flat,
static, extreme black hole solutions in this theory.
