  We continue our investigation of paraorthomodular BZ*-lattices
(PBZ*-lattices), started in \cite{GLP1+,PBZ2,rgcmfp,pbzsums,pbz5}. We shed
further light on the structure of the subvariety lattice of the variety
$\mathbb{PBZL}^{\ast }$ of PBZ*-lattices; in particular, we provide axiomatic
bases for some of its members. Further, we show that some distributive
subvarieties of $\mathbb{PBZL}^{\ast }$ are term-equivalent to well-known
varieties of expanded Kleene lattices or of nonclassical modal algebras. By so
doing, we somehow help the reader to locate PBZ*-lattices on the atlas of
algebraic structures for nonclassical logics.
