Antimicrobial resistance (AMR) poses an ever-increasing challenge to the treatment of infections. AMR mechanisms are commonly associated with AMR genes that are carried on mobile elements, such as plasmids that can move between bacterial lineages. Here we introduce an approach that allows us to reconstruct how plasmids move between bacterial lineages. To do so, we model the co-evolution of chromosomal and plasmid DNA in a Bayesian phylogenetic network approach using a joint coalescent and plasmid transfer process. We apply this new approach to a five-year dataset of Shigella isolates from Melbourne, Australia. Doing so, we reconstruct the gain and loss of small plasmids, and the recent dissemination of a multidrug-resistance plasmid between S. sonnei and S. flexneri lineages in multiple independent events and through steady growth in the prevalence since 2010. This approach has a strong potential to improve our understanding of where AMR-carrying plasmids are introduced and maintained.