  We compute the probability of producing $n$ particles from few colliding
particles in the unbroken $(3+1)$-dimensional $\lambda\phi^4$ theory. To this
end we numerically implement semiclassical method of singular solutions which
works at ${n \gg 1}$ in the weakly coupled regime ${\lambda \ll 1}$. For the
first time, we obtain reliable results in the region of exceptionally large
final state multiplicities ${n\gg \lambda^{-1}}$ where the probability
decreases exponentially with $n$, ${{\cal P}(\mbox{few} \to n) \sim
\exp\{f_\infty(\varepsilon) \, n\}}$, and its slope $f_{\infty}< 0$ depends on
the mean kinetic energy $\varepsilon$ of produced particles. In the opposite
case ${n\ll \lambda^{-1}}$ our data match well-known tree-level result, and
they interpolate between the two limits at $n \sim \lambda^{-1}$. Overall, this
proves exponential suppression of the multiparticle production probability at
${n\gg 1}$ and arbitrary $\varepsilon$ in the unbroken theory. Using numerical
solutions, we critically analyze the mechanism for multiple Higgs boson
production suggested in the literature. Application of our technique to the
scalar theory with spontaneously broken symmetry can eradicate (or confirm) it
in the nearest future.
