This talk presents a regression framework for multivariate claim frequencies that accounts for overdispersion arising from unobserved heterogeneity and for dependencies between claim types that can be positive or negative. The focus is on multivariate count models in which Poisson components are linked through continuous latent effects with continuous marginals combined via copulas. This structure allows flexible dependence modelling and remains identifiable under mild regularity conditions. Estimation is carried out using a Monte Carlo Expectation–Maximization algorithm, which treats the latent variables as missing data and enables maximum likelihood inference when the joint distribution is intractable. A case study on the Wisconsin Local Government Property Insurance Fund shows that the proposed approach captures dependence patterns well and improves predictive performance compared to existing benchmarks. Diagnostic analyses further support the adequacy of the fit. The results highlight the importance of allowing both dispersion and dependence to vary with covariates when assessing and pricing risk in non-life insurance portfolios.