  We find an infinite class of non-supersymmetric multi-center solutions to the
STU model in five-dimensional ungauged supergravity coupled to two vector
multiplets. The solutions are obtained by solving a system of linear equations
on a class of Ricci-scalar-flat K\"ahler manifolds studied by LeBrun. After
imposing an additional U(1) isometry in the base, we solve the axisymmetric
$SU(\infty)$ Toda equation and obtain explicit supergravity solutions
containing arbitrary numbers of 2-cycles with cohomological fluxes of all three
flavors. This improves upon a previous result where only two of the three
fluxes were topologically non-trivial. Imposing regularity and absence of
closed timelike curves, we obtain "bubble equations" highly reminiscent of
those known in the supersymmetric case. Thus we extend much of the analysis
done for BPS bubbling solutions to this new family of non-supersymmetric
bubbling solutions.
