The linearly constrained minimum variance (LCMV) beam-former has been widely employed to extract (a mixture of) multiple desired speech signals from a collection of microphone signals, which are also polluted by other interfering speech signals and noise components. In many practical applications, the LCMV beamformer requires that the subspace corresponding to the desired and interferer signals is either known, or estimated by means of a data-driven procedure, e.g., using a generalized eigenvalue decomposition (GEVD). In practice, however, it often occurs that insufficient relevant samples are available to accurately estimate these subspaces, leading to a beamformer with poor output performance. In this paper we propose a subspace projection-based approach to improve the performance of the LCMV beamformer by exploiting the available data more efficiently. The improved performance achieved by this approach is demonstrated by means of simulation results.