  We apply the numerical conformal bootstrap to correlators of Coulomb and
Higgs branch operators in $4d$ $\mathcal{N}=2$ superconformal theories. We
start by revisiting previous results on single correlators of Coulomb branch
operators. In particular, we present improved bounds on OPE coefficients for
some selected Argyres-Douglas models, and compare them to recent work where the
same cofficients were obtained in the limit of large $r$ charge. There is solid
agreement between all the approaches. The improved bounds can be used to
extract an approximate spectrum of the Argyres-Douglas models, which can then
be used as a guide in order to corner these theories to numerical islands in
the space of conformal dimensions. When there is a flavor symmetry present, we
complement the analysis by including mixed correlators of Coulomb branch
operators and the moment map, a Higgs branch operator which sits in the same
multiplet as the flavor current. After calculating the relevant superconformal
blocks we apply the numerical machinery to the mixed system. We put general
constraints on CFT data appearing in the new channels, with particular emphasis
on the simplest Argyres-Douglas model with non-trivial flavor symmetry.
