Supermassive stars born in pristine environments in the early Universe hold the promise of being the seeds for the supermassive black holes observed as high redshift quasars shortly after the epoch of reionisation. H2 suppression is thought to be crucial in order to negate normal Population III star formation and allow high accretion rates to drive the formation of supermassive stars. Only in the cases where vigorous fragmentation is avoided will a monolithic collapse be successful giving rise to a single massive central object. We investigate the number of fragmentation sites formed in collapsing atomic cooling haloes subject to various levels of background Lyman-Werner flux. The background Lyman-Werner flux manipulates the chemical properties of the gas in the collapsing halo by destroying H2. We find that only when the collapsing gas cloud shifts from the molecular to the atomic cooling regime is the degree of fragmentation suppressed. In our particular case we find that this occurs above a critical Lyman-Werner background of J ∼ 10 J21. The important criterion being the transition to the atomic cooling regime rather than the actual value of J, which will vary locally. Once the temperature of the gas exceeds T & 104 K and the gas transitions to atomic line cooling, then vigorous fragmentation is strongly suppressed.