  The block-orthogonal generalization of the Majumdar-Papapetrou type solutions
for the sigma-model studied earlier are obtained and corresponding solutions
with p-branes are considered. The existence of solutions and the number of
independent harmonic functions is defined by the matrix of scalar products of
vectors $U^s$, governing the sigma-model target space metric. For orthogonal
$U^s$, when target space is a symmetric homogeneous space, the solutions reduce
to the previous ones. Two special classes of solutions with $U^s$ related to
finite dimensional Lie algebras and hyperbolic (Kac-Moody) algebras are singled
out and investigated. The affine Cartan matrices do not arise in the scheme
under consideration. Some examples of obtained solutions and intersection rules
for D=11 supergravity, related D=12 theory and extending them $B_D$-models are
considered. For special multicenter solutions criterions for the existence of
horizon and curvature singularity are found.
