  I describe the \emph{Chiral rings} $R_{3,4}$ for $3$D, $N=4$ supersymmetric
$G$-gauge theory and matter fields in quaternionic representations $E$: first,
by a topological tweak of the construction of arxiv:1601.03586, and second,
more explicitly, by Weyl group descent from the maximal torus. A topological
obstruction is $w_4(E)$ modulo squares, for $R_3$; a secondary obstruction,
from $\eta\cdot E$, may appear for $R_4$. Flatness over the Toda bases allows
their calculation by reduction to $\mathrm{SU}_2$. For some representations, an
Abelianization formula describes the $R$ in terms of the maximal torus and the
Weyl group. This provides an alternative to a recent attempt arxiv:2201.09475.
