We assessed the impacts of co‐occurring invasive plant species on fire regimes and postfire native communities in the Mojave Desert, western USA. We analyzed the distribution and co‐occurrence patterns of three invasive annual grasses (Bromus rubens, Bromus tectorum, and Schismus spp.) known to alter fuel conditions and community structure, and an invasive forb (Erodium cicutarium) which dominates postfire sites. We developed species distribution models (SDMs) for each of the four taxa and analyzed field plot data to assess the relationship between invasives and fire frequency, years postfire, and the impacts on postfire native herbaceous diversity. Most of the Mojave Desert is highly suitable for at least one of the four invasive species, and 76% of the ecoregion is predicted to have high or very high suitability for the joint occurrence of B. rubens and B. tectorum and 42% high or very high suitability for the joint occurrence of the two Bromus species and E. cicutarium. Analysis of cover from plot data indicated two or more of the species occurred in 77% of the plots, with their cover doubling with each additional species. We found invasive cover in burned plots increased for the first 20 years postfire and recorded two to five times more cover in burned than unburned plots. Analysis also indicated that native species diversity and evenness as negatively associated with higher levels of relative cover of the four invasive taxa. Our findings revealed overlapping distributions of the four invasives; a strong relationship between the invasives and fire frequency; and significant negative impacts of invasives on native herbaceous diversity in the Mojave. This suggests predicting the distributions of co‐occurring invasive species, especially transformer species, will provide a better understanding of where native‐dominated communities are most vulnerable to transformations following fire or other disturbances.