Multiple-vehicle crashes involving at least two vehicles constitute over 70% of fatal and injury crashes in the U.S. Moreover, multiple-vehicle crashes involving three or more vehicles (3+) are usually more severe compared with the crashes involving only two vehicles. This study focuses on developing 3+ multiple-vehicle crash severity models for a freeway section using real-time traffic data and crash data for the years 2014–2016. The study corridor is a 111-mile section on I-4 in Orlando, Florida. Crash injury severity was classified as a binary outcome (fatal/severe injury and minor/no injury crashes). For the purpose of identifying the reliable relationship between the 3+ severe multiple-vehicle crashes and the identified explanatory variables, a binary probit model with Dirichlet random effect parameter was used. More specifically, Dirichlet random effect model was introduced to account for unobserved heterogeneity in the crash data. The probit model was implemented using a Bayesian framework and the ratios of the Monte Carlo errors were monitored to achieve parameter estimation convergence. The following variables were found significant at the 95% Bayesian credible interval: logarithm of average vehicle speed, logarithm of average equivalent 10-minute hourly volume, alcohol involvement, lighting condition, and number of vehicles involved (3, or >3) in multiple-vehicle crashes. Further analysis involved analyzing the posterior probability distributions of these significant variables. The study findings can be used to associate certain traffic conditions with severe injury crashes involving 3+ multiple vehicles, and can help develop effective crash injury reduction strategies based on real-time traffic data.