Despite its multivariate nature, independent component analysis (ICA) is generally limited to univariate latents in the sense that each latent component is a scalar process. Independent subspace analysis (ISA), or multidimensional ICA (MICA), is a generalization of ICA which identifies latent independent vector components instead. While ISA/MICA considers multidimensional latent components within a single dataset, our work specifically considers the case of multiple datasets. Independent vector analysis (IVA) is a related technique that also considers multiple datasets explicitly but with a fixed and constrained model. Here, we first show that 1) ISA/MICA naturally extends to the case of multiple datasets (which we call MISA), and that 2) IVA is a special case of this extension. Then we develop an algorithm for MISA and demonstrate its performance on both IVA- and MISA-type problems. The benefit of these extensions is that the vector sources (or subspaces) capture higher order statistical dependence across datasets while retaining independence between subspaces. This is a promising model that can explore complex latent relations across multiple datasets and help identify novel biological traits for intricate mental illnesses such as schizophrenia.