  In this paper a lower bound for the ADM mass is given in terms of the angular
momenta and charges of black holes present in axisymmetric initial data sets
for the Einstein-Maxwell equations. This generalizes the mass-angular
momentum-charge inequality obtained by Chrusciel and Costa to the case of
multiple black holes. We also weaken the hypotheses used in the proof of this
result for single black holes, and establish the associated rigidity statement.
