In this study, a multivariable Generic Model Control (GMC) approach is proposed based on input-output linear-in-parameters time series data-driven models. Adaptation of the model parameters is carried out at every sampling instant. For higher relative degree systems, two different definitions are used for output derivatives, yielding two versions of adaptive GMC for multivariable processes. The performance of the proposed control algorithms is illustrated by application to multivariable semi-batch reactors without and with coolant dynamics for control of temperature and one of the reactant concentrations. The study indicated that the adaptive GMC (AGMC) algorithms for higher relative degree multiple-input and multiple-output (MIMO) systems with a different relative degree have exhibited performance comparable to or better than the phenomenological model-based GMC with respect to both set point tracking and smooth input profiles, and also that the predictive version of AGMC (AGMC-II) has exhibited slightly lower integral square error (ISE) values compared to AGMC-I in case of multivariable semi-batch reactor with coolant dynamics.