  We impose partial-wave unitarity on $2 \to 2$ tree-level scattering processes
to derive constraints on the dimensions of large scalar and fermionic
multiplets of arbitrary gauge groups. We apply our results to scalar and
fermionic extensions of the Standard Model, and also to the Grand Unified
Theories (GUTs) based on the groups $SU(5)$, $SO(10)$, and $E_6$. We find
scenarios within the latter two GUTs that violate the unitarity condition; this
may require a reevaluation of the validity of perturbation theory in those
scenarios.
