  We find a class of non-supersymmetric multi-center solutions of the STU model
of five-dimensional ungauged supergravity. The solutions are determined by a
system of linear equations defined on a four-dimensional K\"ahler manifold with
vanishing Ricci scalar and a U(1) isometry. The most general class of such
K\"ahler manifolds was studied by LeBrun and they have non-trivial 2-cycles
that can support the topological fluxes characteristic of bubbled geometries.
After imposing an additional U(1) symmetry on the base we find explicit
multi-center supergravity solutions. We show that there is an infinite number
of regular multi-center solutions with non-trivial topology that are asymptotic
to the near-horizon limit of a BMPV black hole.
