  Nonclassicality of quantum states is expressed in many shades, the most
stringent of them being a new standard introduced recently in [Phys. Rev. A 89,
062110 (2014)]. This is accomplished by expanding the notion of local hidden
variables (LHV) to generalised local hidden variables (GLHV), which renders
many nonlocal states also classical. We investigate these super-quantum states
(called exceptional in [Phys. Rev. A 89, 062110 (2014)]) in the family of
$SU(2)$ invariant $3 \times N$ level systems. We show that all super-quantum
states admit a universal geometrical description, and that they are most likely
to lie on a line segment in the manifold, irrespective of the value of $N$. We
also show that though the super - quantum states can be highly mixed, its
relative rank with respect to the uniform state is always less than that of a
state which admits a GLHV description.
