  Two correlation functions of Yang-Mills beyond the primitively divergent
ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and
their influence on lower vertices is examined. Their full (transverse) tensor
structure is taken into account. As input, a solution of the full two-point
equations - including two-loop terms - is used that respects the resummed
perturbative ultraviolet behavior. A clear hierarchy is found with regard to
the color structure that reduces the number of relevant dressing functions. The
impact of the two-ghost-two-gluon vertex on the three-gluon vertex is
negligible, which is explained by the fact that all non-small dressing
functions drop out due to their color factors. Only in the ghost-gluon vertex a
small net effect below $2\%$ is seen. The four-ghost vertex is found to be
extremely small in general. Since these two four-point functions do not enter
into the propagator equations, these findings establish their small overall
effect on lower correlation functions.
