  We study the self-consistency problem of the generalized Feynman rule
(nonperturbatively modified vertex of zeroth perturbative order) for the
4-gluon vertex function in the framework of an extended perturbation scheme
accounting for non-analytic coupling dependence through the Lambda scale.
Tensorial structure is restricted to a minimal dynamically closed basis set.
The self-consistency conditions are obtained at one loop, in Landau gauge, and
at the lowest approximation level (r=1) of interest for QCD. At this level,
they are found to be linear in the nonperturbative 4-gluon coefficients, but
strongly overdetermined due to the lack of manifest Bose symmetry in the
relevant Dyson-Schwinger equation. The observed near decoupling from the
2-and-3-point conditions permits least-squares quasisolutions for given
2-and-3-point input within an effective one-parameter freedom. We present such
solutions for N_F=2 massless quarks and for the pure gluon theory, adapted to
the 2-and-3-point coefficients determined previously.
