  To date, the best effort made to simply determine the Coulomb branch global
symmetry of a theory from a $3d$ $\mathcal{N}=4$ quiver is by applying an
algorithm based on its balanced gauge nodes. This often gives the full global
symmetry, but there have been many cases seen where it instead gives only a
subgroup. This paper presents a method for constructing several families of
$3d$ $\mathcal{N}=4$ unitary quivers where the true global symmetry is enhanced
from that predicted by the balance algorithm, motivated by the study of Coulomb
branch Hasse diagrams. This provides a rich list of examples on which to test
improved algorithms for unfailingly identifying the Coulomb branch global
symmetry from a quiver.
