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The study of form factors has many phenomenologically interestingapplications, one of which is Higgs plus gluon amplitudes in QCD. Througheffective field theory techniques these are related to form factors of variousoperators of increasing classical dimension. In this paper we extend ouranalysis of the first finite top-mass correction, arising from the operator${\rm Tr} (F^3)$, from $\mathcal{N}=4$ super Yang-Mills to theories with$\mathcal{N}<4$, for the case of three gluons and up to two loops. We confirmour earlier result that the maximally transcendental part of the associatedCatani remainder is universal and equal to that of the form factor of aprotected trilinear operator in the maximally supersymmetric theory. The termswith lower transcendentality deviate from the $\mathcal{N}=4$ answer by asurprisingly small set of terms involving for example $\zeta_2$, $\zeta_3$ andsimple powers of logarithms, for which we provide explicit expressions.

$\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part II: $0<\mathcal{N}<4$ super Yang-Mills