  We elaborate on the color-kinematics duality for off-shell diagrams in gauge
theories coupled to matter, by investigating the scattering process $gg\to ss,
q\bar q, gg$, and show that the Jacobi relations for the kinematic numerators
of off-shell diagrams, built with Feynman rules in axial gauge, reduce to a
color-kinematics violating term due to the contributions of sub-graphs only.
Such anomaly vanishes when the four particles connected by the Jacobi relation
are on their mass shell with vanishing squared momenta, being either external
or cut particles, where the validity of the color-kinematics duality is
recovered. We discuss the role of the off-shell decomposition in the direct
construction of higher-multiplicity numerators satisfying color-kinematics
identity in four as well as in $d$ dimensions, for the latter employing the
Four Dimensional Formalism variant of the Four Dimensional Helicity scheme. We
provide explicit examples for the QCD process $gg\to q\bar{q}g$.
