Correlated evolution among traits, which can happen due to genetic constraints, ontogeny, and selection, can have an important impact on the trajectory of phenotypic evolution. For example, shifts in the pattern of evolutionary integration may allow the exploration of novel regions of the morphospace by lineages. Here we use phylogenetic trees to study the pace of evolution of several traits and their pattern of evolutionary correlation across clades and over time. We use regimes mapped to the branches of the phylogeny to test for shifts in evolutionary integration while incorporating the uncertainty related to trait evolution and ancestral regimes with joint estimation of all parameters of the model using Bayesian Markov chain Monte Carlo. We implemented the use of summary statistics to test for regime shifts based on a series of attributes of the model that can be directly relevant to biological hypotheses. In addition, we extend Felsenstein's pruning algorithm to the case of multivariate Brownian motion models with multiple rate regimes. We performed extensive simulations to explore the performance of the method under a series of scenarios. Finally, we provide two test cases; the evolution of a novel buccal morphology in fishes of the family Centrarchidae and a shift in the trajectory of evolution of traits during the radiation of anole lizards to and from the Caribbean islands.