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.
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