  We construct a family of examples of pairs of 4d N=2 SCFTs whose graded
Coulomb branch dimensions, Weyl-anomaly coefficients and flavour symmetry
algebras and levels coincide, but which are nonetheless distinct SCFTs. The
difference (detectable by the superconformal index) can occur at arbitrarily
high order. We argue that it is, however, reflected in a difference in the
global form of the flavour symmetry groups.
