This paper describes a method to recover task-related brain sources in the context of multiclass brain--computer interfaces (BCIs) based on noninvasive EEG. We extend the method joint approximate diagonalization (JAD) for spatial filtering using a maximum likelihood framework. This generic formulation: 1) bridges the gap between the common spatial patterns (CSPs) and blind source separation of nonstationary sources; and 2) leads to a neurophysiologically adapted version of JAD, accounting for the successive activations/deactivations of brain sources during motor imagery (MI) trials. Using dataset 2a of BCI Competition IV (2008) in which nine subjects were involved in a four-class two-session MI-based BCI experiment, a quantitative evaluation of our extension is provided by comparing its performance against JAD and CSP in the case of cross-validation, as well as session-to-session transfer. While JAD, as already proposed in other works, does not prove to be significantly better than classical one-versus-rest CSP, our extension is shown to perform significantly better than CSP for cross-validated and session-to-session performance. The extension of JAD introduced in this paper yields among the best session-to-session transfer results presented so far for this particular dataset; thus, it appears to be of great interest for real-life BCIs.