  We compute all of the one-loop corrections that are enhanced, $O(\lambda_i
\lambda_j / 16 \pi^2)$, in the limit $s \gg |\lambda_i | v^2 \gg M_{W}^2$, $s
\gg m_{12}^2$ to all the $2 \to 2$ longitudinal vector boson and Higgs boson
scattering amplitudes in the $CP$-conserving two-Higgs doublet model with a
softly broken $\mathbb{Z}_2$ symmetry. In the two simplified scenarios we
study, the typical bound we find is $|\lambda_i(s)| \lessapprox 4$.
