Advanced model-based control strategies, e.g., model predictive control, can offer superior control of key process variables for multiple-input multiple-output systems. The quality of the system model is critical to controller performance and should adequately describe the process dynamics across its operating range while remaining amenable to fast optimization. This work articulates an integrated system identification procedure for deriving black-box nonlinear continuous-time multiple-input multiple-output system models for nonlinear model predictive control. To showcase this approach, five candidate models for polynomial and interaction features of both output and manipulated variables were trained on simulated data and integrated into a nonlinear model predictive controller for a highly nonlinear continuous stirred tank reactor system. This procedure successfully identified system models that enabled effective control in both servo and regulator problems across wider operating ranges. These controllers also had reasonable per-iteration times of ca. 0.1 s. This demonstration of how such system models could be identified for nonlinear model predictive control without prior knowledge of system dynamics opens further possibilities for direct data-driven methodologies for model-based control which, in the face of process uncertainties or modelling limitations, allow rapid and stable control over wider operating ranges.