We consider a model for phase separation of a multi-component alloy with non-smooth free energyand a degenerate mobility matrix. In addition to showingwell-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in orderto be applicable to a logarithmic free energy.Finally numerical experiments with three components in one and two space dimensions are presented.