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.
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