We present an extension of the generalized RAS (GRAS) technique to a multi-regional (MR) or multi-national setting. The framework is applicable to updating/regionalizing/balancing any partitioned matrix that needs to conform to new row sums, column sums and additional non-overlapping aggregation constraints. The technique, which we refer to as MR-GRAS, also handles non-exhaustive constraints, in which case the missing values are endogenously generated in the updating process. We derive the closed-form solution of MR-GRAS, propose a simple iterative algorithm for its computation, and discuss the main analytical properties of the method as well as the normalization and interpretation of MR-GRAS multipliers. From a wide range of possible MR-GRAS applications, several updating frameworks of national and interregional supply and use tables are examined.