  Stationary axisymmetric systems of two extreme Kerr sources separated by a
massless strut, which arise as subfamilies of the well-known Kinnersley-Chitre
solution, are studied. We present explicit analytical formulas for the
individual masses and angular momenta of the constituents and establish the
range of the parameters for which such systems can be regarded as describing
black holes. The mass-angular momentum relations and the interaction force in
the black-hole configurations are also analyzed. Furthermore, we construct a
charging generalization of the Kinnersley-Chitre metric and, as applications of
the general formulas obtained, discuss two special cases describing a pair of
identical co- and counterrotating extreme Kerr-Newman black holes kept apart by
a conical singularity. From our analysis it follows in particular that the
equality $m^2-a^2-e^2=0$ relating the mass, angular momentum per unit mass and
electric charge of a single Kerr-Newman extreme black hole is no longer
verified by the analogous extreme black-hole constituents in binary
configurations.
