Decomposition of magnetotelluric data into a local galvanic 3D distortion matrix and a regional 2D Earth caused a quantum leap in our understanding of complex data and our ability to handle those data. The Groom-Bailey method is the most widely adopted tensor decomposition approach, and rightly so given its physical basis and its separation of distortion parameters into determinable and indeterminable parts. However, on occasion the 3D over 2D (3D/2D) decomposition fails in that the misfit of the model to the data is far greater than the data errors permit, and this failure is due to either the distortion model being invalid or to inappropriately small error estimates for the data. In this paper we describe and demonstrate our attempts to extend MT tensor decomposition to local galvanic 3D distortion of regional 3D data (3D/3D). There are insufficient data to accomplish this uniquely for a single MT site, so some approximations must be made. The approach we use is to assume that two neighboring sites sense the same regional structure if they are sufficiently close compared to the skin depth to the structure, but that the two sites have differing galvanic distortion matrices. We use a decomposition method similar to the Groom-Bailey one, but with a different parameterization, and we solve the problem using a Newton method. We demonstrate the method to a synthetic data set, and highlight the difficulties that results as a consequence of inherent parameter-resolution instabilities.