Multivariate age-period-cohort models have recently been proposed for the analysis of heterogeneous time trends. For a fully Bayesian analysis, Gaussian Markov random field (GMRF) priors are typically used. However, standard GMRF priors do not account for a potential dependence between outcomes. We present an extended approach based on correlated smoothing priors and corre-lated overdispersion parameters. Algorithmic routines are based on either Markov chain Monte Carlo or integrated nested Laplace approximations. Results are discussed for data on female mortality in Denmark and Norway and compared by means of DIC, proper scoring rules and the marginal likelihood.