  We revisit the multi-loop structure of the anomalous-dimension matrix
governing the infrared divergences of massless $n$-particle scattering
amplitudes in non-abelian gauge theories. In particular, we derive its most
general form at four-loop order, significantly simplifying corresponding
expressions given previously. By carefully reevaluating the constraints imposed
by two-particle collinear limits, we find that at four-loop order color
structures involving $d_R^{abcd}$, the symmetrized trace of four group
generators, appear along with cusp logarithms $\ln[\mu^2/(-s_{ij})]$. As a
consequence, naive Casimir scaling of the cusp anomalous dimensions associated
with the quark and gluon form factors is violated, while a generalized form of
Casimir scaling still holds. Our results provide an important ingredient for
resummations of large logarithms in $n$-jet cross sections with
next-to-next-to-next-to leading logarithmic (N$^3$LL) accuracy.
