An optimal Bonus-Malus System (BMS) based on both the number of accidents and the severity of each accident was developed by Frangos and Vrontos (2001). In this paper we extend the work of Frangos and Vrontos (2001), Lemaire (1995) and Dionne and Vannasse (1989, 1992) using finite mixture models. For the frequency component we employ a finite Poisson, Delaporte and Negative Binomial mixture, while for the severity component we employ a finite Exponential, Gamma, Weibull and Generalised Beta mixture, updating the posterior probability. We also consider the case of a finite Negative Binomial mixture and a finite Pareto mixture updating the posterior mean. The generalized BMS we propose takes into account both the a priori and a posteriori characteristics of each policyholder. In the above setup optimality is achieved by minimizing the insurer's risk.