Knowledge of who infected whom during an outbreak of an infectious disease is important to determine risk factors for transmission and to design effective control measures. Both whole-genome sequencing of pathogens and epidemiological data provide useful information about the transmission events and underlying processes. Existing models to infer transmission trees usually assume that the pathogen is introduced only once from outside into the population of interest. However, this is not always true. For instance, SARS-CoV-2 is suggested to be introduced multiple times in mink farms in the Netherlands from the SARS-CoV-2 pandemic among humans. Here, we developed a Bayesian inference method combining whole-genome sequencing data and epidemiological data, allowing for multiple introductions of the pathogen in the population. Our method does not a priori split the outbreak into multiple phylogenetic clusters, nor does it break the dependency between the processes of mutation, within-host dynamics, transmission, and observation. We implemented our method as an additional feature in the R-package phybreak. On simulated data, our method correctly identifies the number of introductions, with an accuracy depending on the proportion of all observed cases that are introductions. Moreover, when a single introduction was simulated, our method produced similar estimates of parameters and transmission trees as the existing package. When applied to data from a SARS-CoV-2 outbreak in Dutch mink farms, the method provides strong evidence for independent introductions of the pathogen at 13 farms, infecting a total of 63 farms. Using the new feature of the phybreak package, transmission routes of a more complex class of infectious disease outbreaks can be inferred which will aid infection control in future outbreaks.