  Kaneyama and Klyachko have shown that any torus equivariant vector bundle of
rank $r$ over $\mathbb{CP}^n$ splits if $r < n$. In particular, any such bundle
is not slope stable. In contrast, we provide explicit examples of stable
equivariant reflexive sheaves of rank $r$ on any polarised toric variety $(X,
L)$, for $2 \leq r < \mathrm{dim}(X) + \mathrm{rank}(\mathrm{Pic}(X))$, and
show that the dimension of their singular locus is strictly bounded by $n - r$.
