  Connected $N$-point amplitudes in quantum field theory are enhanced by a
factor of $N!$ in appropriate regimes of kinematics and couplings, but the
non-perturbative analysis of this for collider physics applications is subtle.
We resolve this question for $N$-point correlation functions of cosmological
perturbations in multifield inflation, and comment on its application to
primordial non-Gaussianity. We find that they are calculably $N!$-enhanced
using a simple model for the mixing of the field sectors which leads to a
convolution of their probability distributions. This effect leads to
model-dependent but interesting prospects for enhanced observational
sensitivity.
