This paper extends the method introduced by Rollins et al. (ISA Trans. 1998,36,293) to multiple-input, multiple-output systems that give an exact closed-form solution to continuous-time Hammerstein processes written in terms of differential equations and nonlinear inputs. This ability is demonstrated on a theoretical nonlinear Hammerstein process of complex dynamics where perfect identification of the closed-form model is assumed. This paper then demonstrates the simplicity of the proposed identification procedure to obtain an accurate estimate of the exact model using a theoretical Hammerstein model. A powerful attribute of this methodology is the ability to make full use of the statistical design of experiments for optimal data collection and accurate parameter estimation. Application of the proposed method is demonstrated on a household clothes dryer with four input and five output variables. Only 27 trials (input changes) of a central composite design were needed for accurate model development of all five outputs over the input space, and the accurate predictive performance is demonstrated.