This study sought to determine the degree to which the auditory system can perform simultaneous across‐frequency analyses on concurrent, but independent, modulation patterns. This was tested by measuring detection of a multicomponent signal presented against a background comprised of multiple modulation patterns. The results indicated that independent comodulation masking releases (CMRs) could occur simultaneously, but only if the independent modulation patterns were restricted to relatively discrete frequency regions. Moreover, the analysis accomplished in each region did not appear to be optimal. This suggests that there are limits to the independence with which simultaneous across‐frequency analyses can be performed.