Successful implementation of optimization-driven control techniques, such as model predictive control (MPC), is highly dependent on an accurate and detailed model of the process. As complexity in the system increases, linear approximation used in MPC may result in poor performance since a critical operating point is valid in only a small neighborhood of operation. To address this problem, this paper proposes a collaborative approach that combines linear and data-based models to predict state variables individually. The outputs of these models, along with constraints, are then incorporated into the MPC algorithm. For data-based process model, a multi-layered feed-forward network is used. Additionally, the offset-free technique is applied to eliminate steady-state errors resulting from model-process mismatch. To demonstrate the results, a binary distillation column process which is multivariable and inherently nonlinear is chosen as testbed. We compare the performance of the proposed method to MPC using the full nonlinear model and also to single-model MPC methods for both the linear model and neural network model. We show that the proposed method is only slightly suboptimal with respect to the best available performance and greatly improves over individual methods. In addition, the computational load is reduced when compared to the full nonlinear MPC.