A Bayesian model for granular insurance claim amounts is proposed. It accounts for the multi-level, multivariate features of individual claims, e.g., multiple claimants for the same event, each of whom may receive benefits under different coverages. To avoid sampling bias induced when relying only on closed files, a multiple imputation procedure exploiting open file data is proposed. For a given claim, the combination of coverages under which payments are made forms a type which is modeled with multinomial regression. The presence of legal and claims expert fees follows a logistic regression, given the type. The strictly positive severities are then modeled with log skewed normal regressions linked by a Student t copula. The Bayesian framework yields a predictive distribution for the amounts paid, including parameter risk and process risk, while handling missing covariates and open files. The approach is illustrated with Accident Benefits car insurance claims from a large Canadian company.