The universal family is the set of cuspidal automorphic representations of bounded analytic conductor on ${\rm GL}_n$ over a number field. We prove an asymptotic for the universal family, under a spherical assumption at the archimedean places when $n\geqslant 3$. We interpret the leading term constant geometrically and conjecturally determine the underlying Sato--Tate measure. Our methods naturally provide uniform Weyl laws with explicit level savings and strong quantitative bounds on the non-tempered discrete spectrum for ${\rm GL}_n$.