  We review some known results on the superintegrability of monopole systems in
the three-dimensional (3D) Euclidean space and in the 3D generalized Taub-NUT
spaces. We show that these results can be extended to certain curved
backgrounds that, for suitable choice of the domain of the coordinates, can be
related via conformal transformations to systems in Taub-NUT spaces. These
include the multi-fold Kepler systems as special cases. The curvature of the
space is not constant and depends on a rational parameter that is also related
to the order of the integrals. New results on minimal superintegrability when
the electrostatic potential depends on both radial and angular variables are
also presented.
