Consistent frameworks of quantum gravity often predict the existence of large numbers of ultralight pseudoscalar degrees of freedom, forming the phenomenological landscape of the String Axiverse. The complexity of the extra-dimensional compactification manifolds and vacua determine that these fields could possess parameters with cosmologically significant scales, which span many decades. Astrophysical observations of stellar binary and supermassive black hole systems can be used to exclude the existence of certain ultralight massive bosons, via the superradiance phenomenon. In this work it is shown how these measurements can be used to constrain properties of statistical distributions for the masses of multiple bosonic field theories, inspired by axion field alignment models and an explicit realisation of the string axiverse in M-theory. Such a methodology can exclude $N_{\rm ax} \geq 30$ axion-like fields with a range of mass distribution widths and central values spanning many orders of magnitude, covering axion phenomenologies important to the dark sector and grand unified theories. This is demonstrated for several examples of axions in string theory and M-theory, where the mass distributions in certain cases take universal forms found in random matrix theory.