One way of enhancing the dexterity of powered myoelectric prostheses is via proportional and simultaneous control of multiple degrees-of-freedom (DOFs). Recently, it has been demonstrated that the reconstruction of finger movement is feasible by using features of the surface electromyogram (sEMG) signal. In such paradigms, the number of predictors and target variables is usually large, and strong correlations are present in both the input and output domains. Synergistic patterns in the sEMG space have been previously exploited to facilitate kinematics decoding. In this work, we propose a framework for simultaneous input-output dimensionality reduction based on the generalized eigenvalue problem formulation of multiple linear regression (MLR). We demonstrate that the proposed methodology outperforms simultaneous input-output dimensionality reduction based on principal component analysis (PCA), while the prediction accuracy of the full rank regression (FRR) method can be achieved by using only a few relevant dimensions.