  We study the stratification of the singular locus of four dimensional
$\mathcal{N}=2$ Coulomb branches. We present a set of self-consistency
conditions on this stratification which can be used to extend the
classification of scale-invariant rank 1 Coulomb branch geometries to two
complex dimensions, and beyond. The calculational simplicity of the arguments
presented here stems from the fact that the main ingredients needed -- the rank
1 deformation patterns and the pattern of inclusions of rank 2 strata -- are
discrete topological data which satisfy strong self-consistency conditions
through their relationship to the central charges of the SCFT. This
relationship of the stratification data to the central charges is used here,
but is derived and explained in a companion paper by one of the authors. We
illustrate the use of these conditions by re-analyzing many previously-known
examples of rank 2 SCFTs, and also by finding examples of new theories. The
power of these conditions stems from the fact that for Coulomb branch
stratifications a conjecturally complete list of physically allowed "elementary
slices" is known. By contrast, constraining the possible elementary slices of
symplectic singularities relevant for Higgs branch stratifications remains an
open problem.
