This paper aims to design linear precoders for signal superposition at the base stations of non-orthogonal multiple access multiple-input multiple-output multi-cellular systems to maximize the overall sum throughput subject to the users' quality-of-service requirements, which are imposed independently on the users' channel conditions. This design problem is formulated as the maximization of a highly nonlinear and nonsmooth function subject to nonconvex constraints, which is very computationally challenging. A path-following algorithm for its solution, which invokes only a simple convex problem of moderate dimension at each iteration, is developed. Generating a sequence of improved points, this algorithm converges at least to a local optimum. Numerical results are then provided to demonstrate its merit.