The plot of allowed p and D values for p-brane solitons in D-dimensional supergravity is the same whether the solitons are extremal or nonextremal. One of the useful tools for relating different points on the plot is vertical dimensional reduction, which is possible if periodic arrays of p-brane solitons can be constructed. This is straightforward for extremal p-branes, since the no-force condition allows arbitrary multicenter solutions to be constructed in terms of a general harmonic function on the transverse space. This has also been shown to be possible in the special case of nonextremal black holes in D=4 arrayed along an axis. In this paper, we extend previous results to include multiscalar black holes, and dyonic black holes. We also consider their oxidation to higher dimensions, discuss general procedures for constructing the solutions and study their symmetries.