Extremely female-biased sex ratios of parasitoid wasps in multiple-foundress groups challenges evolutionary theory which predicts diminishing bias as foundress numbers increase. Recent theory based on foundress cooperation has achieved qualitative rather than quantitative success in explaining bias among parasitoids in the genus Sclerodermus. Here, we develop an explanation, expanding the theory of local mate competition, based on the observation that male production seems dominated by some foundresses within groups. Two sex ratio effects arise from such reproductive dominance: an immediate effect via suppression of male production, and a long-term evolutionary response to reproductive skew. We analyze the outcome of these effects at the individual and group level, the latter being more readily observable. Three model scenarios are analyzed: (1) random killing of developing sons in a group by all foundresses, without reproductive skew, (2) the development of reproductive dominance by some foundresses after sex allocation decisions by all foundresses have been implemented, and (3) reproductive dominance within foundress groups before sex allocation decisions are implemented. The 3 scenarios have subtly different implications for sex ratio evolution, with Models 2 and 3 being novel additions to theory, showing how reproductive dominance can alter the outcome of sex ratio evolution. All models match observations in their outcomes better than other recently proposed theory, but Models 2 and 3 are closest to observations in their underlying assumptions. Further, Model 2 shows that differential offspring mortality after parental investment can influence the primary sex ratio even when random with respect to parental and offspring characters, but targeted at entire clutches. The novel models are solved for both diploid and haplodiploid genetic systems, and confirmed with simulations. Overall, these models provide a feasible explanation for the extremely female-biased sex ratios produced by multi-foundress groups and expand the scope of local mate competition theory to consider reproductive dominance.