  We consider Shiraishi's metrics on the moduli space of extreme black holes.
We interpret the simplification in the pattern of N-body interactions that he
observed in terms of the recent picture of black holes in four and five
dimensions as composites, made up of intersecting branes. We then show that the
geometry of the moduli space of a class of black holes in five and nine
dimensions is hyper-K\"ahler with torsion, and octonionic-K\"ahler with
torsion, respectively. For this, we examine the geometry of point particle
models with extended world-line supersymmetry and show that both of the above
geometries arise naturally in this context. In addition, we construct a large
class of hyper-K\"ahler with torsion and octonionic-K\"ahler with torsion
geometries in various dimensions. We also present a brane interpretation of our
results.
