  We determine the structure of the $*$-Lie superalgebra generated by a set of
carefully chosen natural operators of an orientable WSD manifold of rank three.
This Lie superalgebra is formed by global sections of a natural Lie
superalgebra bundle, and turns out to be a product of $\mathbf{sl}(4,\C)$ with
the full special linear superalgebras of some graded vector spaces isotypical
with respect to a natural action of $\mathbf{so}(3,\R)$. We provide an explicit
description of one of the real forms of this superalgebra, which is
geometrically natural being made of $\mathbf{so}(3,\R)$-invariant operators
which preserve the Poincar\'e (odd Hermitean) inner product on the bundle of
forms.
