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 a
chieved via enhanced Wilson lines that are supplied with the spin-dependent Pauli term $sim F^{mu u}[gamma_mu, gamma_ u]$, 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.
