  We study non-BPS black hole solutions to ungauged supergravity with 8
supercharges coupled to vector multiplets in four and five dimensions. We
identify a large class of five dimensional non-BPS solutions, which we call
"almost BPS", that are supersymmetric on local patches and satisfy a first
order flow governed by harmonic functions. By dimensional reduction, they give
rise to new non-BPS solutions in four dimensions. These solutions allow for
some nontrivial asymptotic moduli and multiple centres, similar to their
globally supersymmetric cousins. We explicitly discuss a single centre and a
two centre example.
