  We extend our investigation on Couch-Torrence conformal inversions of BHs and
D-branes in various directions. We analyse asymptotically flat rotating charged
BHs in $D=4$, in particular extremal rotating BHs in STU supergavity, and find
invariance for special choices of the charges. Due to the dependence of the
critical radii on the impact parameter(s), the relation between the scattering
angle for geodesics outside the photon-halo and the in-spiralling angle for
geodesics inside the photon-halo is modified by the inclusion of a boundary
term. We also consider rotating BHs in $D=5$ and rotating D3-branes and find
invariance under generalised Couch-Torrence inversions for special choices of
the angular momenta. Alas we don't find any similar symmetry for smooth
horizonless geometries. Moreover, relying on the surprising connection between
classical BH perturbation theory and quantum Seiberg-Witten curves for ${\cal
N}=2$ SYM theories, we study scalar wave equations in these backgrounds and
identify the near super-radiant modes produced in near-extremal BH mergers.
Finally, we study scalar fluctuations around Kerr-Newman BHs in AdS$_4$ and
find stringent conditions for generalised Couch-Torrence symmetry that are
relaxed in the extremal case or by allowing a rescaling of the wave function.
