The numbers of cars in a household has an important effect on its travel behavior (e.g., choice of number of trips, mode to work, and non-work destinations), hence car ownership modeling is an essential component of any travel demand forecasting effort. In this paper we report on a random effects multinomial probit model of car ownership level, estimated using longitudinal data collected in the Netherlands. A Bayesian approach is taken and the model is estimated by means of a modification of the Gibbs sampling with data augmentation algorithm considered by McCulloch and Rossi (1994). The modification consists in performing, after each Gibbs sampling cycle, a Metropolis step along a direction of constant likelihood. An examination of the simulation output illustrates the improved performance of the resulting sampler.