As the number of biological invasions increases, the potential for invader-invader interactions also rises. The effect of multiple invaders can be superadditive (invasional meltdown), additive, or subadditive (invasional interference); which of these situations occurs has critical implications for prioritization of management efforts. Carduus nutans and C. acanthoides, two congeneric invasive weeds, have a striking, segregated distribution in central Pennsylvania, U.S.A. Possible hypotheses for this pattern include invasion history and chance, direct competition, or negative interactions mediated by other species, such as shared pollinators. To explore the role of resource competition in generating this pattern, we conducted three related experiments using a response-surface design throughout the life cycles of two cohorts. Although these species have similar niche requirements, we found no differential response to competition between conspecifics vs. congeners. The response to combined density was relatively weak for both species. While direct competitive interactions do not explain the segregated distributional patterns of these two species, we predict that invasions of either species singly, or both species together, would have similar impacts. When prioritizing which areas to target to prevent the spread of one of the species, it is better to focus on areas as yet unaffected by its congener; where the congener is already present, invasional interference makes it unlikely that the net effect will change.