Releasing mosquitoes transinfected with the endosymbiotic bacterium Wolbachia is a novel strategy for interrupting vector-borne pathogen transmission. Following its success in controlling arboviruses spread by Aedes aegypti, this technology is being adapted for anopheline malaria vectors. However, antagonistic interactions between Wolbachia and naturally resident Asaia bacteria in malaria vectors have been demonstrated experimentally, potentially jeopardising Wolbachia biocontrol. We developed the first mathematical model accounting for interspecific competition between endosymbionts to assess the feasibility of this novel strategy for controlling malaria. First, Asaia prevalences among natural mosquito populations were compared with simulations parametrized with rates of Asaia transmission reported from laboratory studies. Discrepancies between projections and natural Asaia prevalences indicated potential overestimation of Asaia transmissibility in artificial laboratory settings. With parametrization that matches natural Asaia prevalence, simulations identified redundancies in Asaia's many infection routes (vertical, sexual and environmental). This resilience was only overcome when Wolbachia conferred very high resistance to environmental infection with Asaia, resulting in Wolbachia fixation and Asaia exclusion. Wolbachia's simulated spread was prevented when its maternal transmission was impeded in coinfected mosquitoes and the pre-control Asaia prevalence was beyond a threshold of 60-75%. This theoretical assessment highlights critical next steps in laboratory experiments to inform this strategy's feasibility.