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∼10−3 Z⊙ 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⊙ yr−1 approximately two-thirds of these haloes have metallicities of Z>10−3 Z⊙. 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.