  We investigate which 4-derivative extensions of Einstein-Maxwell theory admit
multi-extremal black hole solutions with gravitational force balanced by
Coulomb force. We obtain a set of constraints on the 4-derivative couplings by
exploring various probe limits in multi-black hole systems. It turns out that
these constraints are tighter than those needed to protect the mass-charge
ratio of extremal black holes from higher derivative corrections. In fact, they
are so strong that the Majumdar-Papapetrou multi-black solutions are unmodified
by the force-free combinations of the 4-derivative couplings. Explicit examples
of such 4-derivative couplings are given in 4- and 5-spacetime dimensions.
Interestingly these include curvature-squared supergravity actions and the
quasi-topological $F^4$ term.
