Parasitic organisms have large impacts on wildlife, livestock, and human health, however, little is known about ecological and biological factors influencing their host range. When single-host mites are shifted to new hosts, they are likely to become more virulent and cause epidemics as new hosts may lack natural defenses against new parasites (high epidemic risk). Here, we assembled the largest and complete dataset on mites permanently parasitic on mammals and conducted an analysis of factors affecting the probability of single-host parasites becoming multi-hosts, while accounting for potentially unobserved host-parasite links and class imbalance. We identified statistically significant predictors related to parasites (5 variables), hosts (2), climate (2), and habitat disturbance (1). Among mite-related variables, the most important was the proximity to the host immune system which was correlated with the mouthpart morphology. The accuracy of predicting the multi-host risk group was estimated at 0.721. When our model was used for forecasting, it identified Chiroptera (bats) and Carnivora as hosts having the largest number of parasites belonging to the multi-host risk group category. Of them, several single-host bat parasitic species of Notoedres were identified as having the potential to become multi-hosts that are probably capable of causing an epidemic. Our study provides a robust quantitative framework showing how ecological and biological factors can affect the ability of a single-host parasite to become multi-host.