  We classify orbifold geometries which can be interpreted as moduli spaces of
four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2
(complex dimension 6). The large majority of the geometries we find correspond
to moduli spaces of known theories or discretely gauged version of them.
Remarkably, we find 6 geometries which are not realized by any known theory, of
which 3 have an $\mathcal{N}=2$ Coulomb branch slice with a non-freely
generated coordinate ring, suggesting the existence of new, exotic
$\mathcal{N}=3$ theories.
