  We revisit the novel symmetries in $\mathcal{N}$ = 2 supersymmetric (SUSY)
quantum mechanical (QM) models by considering specific examples of coupled
systems. Further, we extend our analysis to a general case and list out all the
novel symmetries. In each case, we show the existence of two sets of discrete
symmetries that correspond to the Hodge duality operator of differential
geometry. Thus, we are able to provide a proof of the conjecture which points
out the existence of more than one set of discrete symmetry transformations
corresponding to the Hodge duality operator. Moreover, we derive on-shell
nilpotent symmetries for a generalized superpotential within the framework of
supervariable approach.
