  We consider dominant 3-, 4-, and 5-loop contributions to $\lambda$, the
quartic scalar coupling-constant's $\beta$-function in the Standard Model. We
find that these terms accelerate the evolution of $\lambda$ to nonperturbative
values, thereby lowering the unification bound for which scalar-couplings are
still perturbative. We also find that these higher order contributions imply a
substantial lowering of $\lambda$ itself before the anticipated onset of
nonperturbative physics in the Higgs sector.
