  The formation of supermassive stars has generally been studied under the
assumption of rapid accretion of pristine metal-free gas. Recently it was
found, however, that gas enriched to metallicities up to $Z \sim 10^{-3}$
Z$_{\odot}$ can also facilitate supermassive star formation, as long as the
total mass infall rate onto the protostar remains sufficiently high. We extend
the analysis further by examining how the abundance of supermassive star
candidate haloes would be affected if all haloes with super-critical infall
rates, regardless of metallicity were included. We investigate this scenario by
identifying all atomic cooling haloes in the Renaissance simulations with
central mass infall rates exceeding a fixed threshold. We find that among these
haloes with central mass infall rates above 0.1 M$_{\odot}$ yr$^{-1}$
approximately two-thirds of these haloes have metallicities of $Z > 10^{-3}$
Z$_{\odot}$. If metal mixing within these haloes is inefficient early in their
assembly and pockets of metal-poor gas can remain then the number of haloes
hosting supermassive stars can be increased by at least a factor of four.
Additionally the centres of these high infall-rate haloes provide ideal
environments in which to grow pre-existing black holes. Further research into
the (supermassive) star formation dynamics of rapidly collapsing haloes, with
inhomogeneous metal distributions, is required to gain more insight into both
supermassive star formation in early galaxies as well as early black hole
growth.
