Werner deconvolution has been widely used for at least 30 years for rapid interpretation of magnetic data. Since 1993, a multiple-source generalization of the method has been known, and at least two implementations of the algorithm are in use. Recently, Werner deconvolution has been extended to three dimensions through the use of generalized Hilbert transforms. In this paper, a multiple-source extension of the 3D Werner algorithm is developed which also generalizes the 2D multiple-source algorithm. The implementation of this algorithm is tested on both 3D multiple-source synthetic data, for which good agreement with the model is obtained, and on complex data from the Albuquerque basin, which yields results corresponding well with other interpretations and with known geology.