  For N \ge 2 supergravities, BPS black hole solutions preserving four
supersymmetries can be superposed linearly, leading to well defined solutions
containing an arbitrary number of such BPS black holes at arbitrary positions.
Being stationary, these solutions can be understood via associated non-linear
sigma models over pseudo-Riemaniann spaces coupled to Euclidean gravity in
three spatial dimensions. As the main result of this paper, we show that
whenever this pseudo-Riemanniann space is an irreducible symmetric space G/H*,
the most general solutions of this type can be entirely characterised and
derived from the nilpotent orbits of the associated Lie algebra Lie(G). This
technique also permits the explicit computation of non-supersymmetric extremal
solutions which cannot be obtained by truncation to N=2 supergravity theories.
For maximal supergravity, we not only recover the known BPS solutions depending
on 32 independent harmonic functions, but in addition find a set of non-BPS
solutions depending on 29 harmonic functions. While the BPS solutions can be
understood within the appropriate N=2 truncation of N=8 supergravity, the
general non-BPS solutions require the whole field content of the theory.
