Part I of this series of three papers handles the identification of single input single output Box-Jenkins models on arbitrary frequency grids in an open and closed loop setting. Part II discusses the computational aspects and illustrates the theory on simulations and a real life problem. This paper extends the results of Parts I and II to multiple input multiple output systems. Contrary to the classical time domain approach, the presented technique does not require symbolic calculus for multiple output polynomial Box-Jenkins models. (c) 2007 Elsevier Ltd. All rights reserved.