  The (n+1)-sphere contains a simple family of constant mean curvature (CMC)
hypersurfaces which are products of lower-dimensional spheres called the
generalized Clifford hypersurfaces. This paper demonstrates that new,
topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring
generalized Clifford tori connected to each other by small catenoidal bridges
at a sufficiently symmetric configuration of points can be constructed by
perturbative PDE methods. That is, one can create an approximate solution by
gluing a rescaled catenoid into the neighbourhood of each point; and then one
can show that a perturbation of this approximate hypersurface exists which
satisfies the CMC condition. The results of this paper generalize those of the
authors in math.DG/0511742.
