  We refine our previous proposal for systematically classifying 4d rank-1
$\mathcal N=2$ SCFTs by constructing their possible Coulomb branch geometries.
Four new recently discussed rank-1 theories, including novel $\mathcal{N}=3$
SCFTs, sit beautifully in our refined classification framework. By arguing for
the consistency of their RG flows we can make a strong case for the existence
of at least four additional rank-1 SCFTs, nearly doubling the number of known
rank-1 SCFTs.
  The refinement consists of relaxing the assumption that the flavor symmetries
of the SCFTs have no discrete factors. This results in an enlarged (but finite)
set of possible rank-1 SCFTs. Their existence can be further constrained using
consistency of their central charges and RG flows.
