At sufficiently high energies the production of a very large number of particles is kinematically allowed. In some scenarios, tree-level multiparticle amplitudes enter the regime of large-order perturbation theory and hence require a careful investigation. In this talk, we will demonstrate that in scalar quantum field theories, where suitably resummed perturbative expansions are expected to capture all relevant physical effects, perturbation theory may still suffer from severe shortcomings at very high energies. We will address this regime in the general setting of effective field theory and argue that higher-dimensional operators may universally amount to exponentially growing contributions to multiparticle rates