  We introduce a class of Higgs-branch RG flows in theories of class-S, which
flow between $d=4$ $\mathcal{N}=2$ SCFTs of the same ADE type. We discuss two
applications of this class of RG flows: 1) determining the current-algebra
levels in SCFTs where they were previously unknown - a program we carry out for
the class-S theories of type $E_6$ and $E_7$ - and 2) constructing a multitude
of examples of pairs of $\mathcal{N}=2$ SCFTs whose "conventional invariants"
coincide. We disprove the conjecture of [1] that the global form of the flavour
symmetry group is a reliable diagnostic for determining when two such theories
are isomorphic.
