The prediction of insurance liabilities often requires aggregating experience of loss payment from multiple insurers. The resulting data set of intercompany loss triangles displays a multilevel structure of claim development where a portfolio consists of a group of insurers, each insurer several lines of business, and each line various cohorts of claims. In this article, we propose a Bayesian hierarchical model to analyze intercompany claim triangles. A copula regression is employed to join multiple triangles of each insurer, and a hierarchical structure is specified on major parameters to allow for information pooling across insurers. Numerical analysis is performed for an insurance portfolio of multivariate loss triangles from the National Association of Insurance Commissioners. We show that prediction is improved through borrowing strength within and between insurers based on training and holdout observations.