  In a spontaneously broken gauge theory we consider (sub)-processes in which
one virtual intermediate state (it can be a Higgs or a gauge field) produces
many on-shell Higgses and massive vector bosons. In the kinematic regime where
all final states are produced on their mass threshold, we show how to compute
iteratively all tree-level amplitudes ${\cal A}_{1\to n+m}$ involving an
arbitrary number $n$ of Higgs bosons and $m$ of longitudinal vector bosons in
the final state, and list the amplitudes coefficients for up to $n=32$ and
$m=32$. We find that these amplitudes exhibit factorial growth not only in the
number of scalar fields, but also in the number of longitudinal gauge fields,
${\cal A}_{1\to n+m} \sim n! \,m!$. This growth is not expected to disappear at
loop-level in the fixed-order perturbation theory. We conclude that at energies
accessible at the next generation of hadron colliders, such as the 50-100 TeV
FCC, where $\sqrt{\hat{s}}$ is sufficient to produce $\gg 1/\alpha_W$ of $W,Z$
and $H$, perturbation theory breaks down when applied to the multiparticle
electroweak production, at least near the kinematic multiparticle mass
threshold where the electroweak gauge-Higgs sector becomes strongly coupled.
