  We discuss the possibility of non-minimal gauge invariance of
transverse-momentum-dependent parton densities (TMDs) that allows direct access
to the spin degrees of freedom of fermion fields entering the operator
definition of (quark) TMDs. This is achieved via enhanced Wilson lines that are
supplied with the spin-dependent Pauli term $\sim F^{\mu\nu}[\gamma_\mu,
\gamma_\nu]$, thus providing an appropriate tool for the "microscopic"
investigation of the spin and color structure of TMDs. We show that this
generalization leaves the leading-twist TMD properties unchanged but modifies
those of twist three by contributing to their anomalous dimensions. We also
comment on Collins' recent criticism of our approach.
