Interpolating or predicting data is of utmost importance in machine learning, and Gaussian Process Regression is one of the numerous techniques that are often used in practice. In this paper, we consider the case of multi-input and multi-output data. A simple Joint Kriging model is proposed, where common combination weights are applied to all output variables at the same time. This drastically reduces the number of hyperparameters to be optimised while keeping nice interpolating properties. An original constraint on predicted values is also introduced, useful for considering external information or adverse scenarios. Finally, it is shown that, when applied to membership degrees, the model is especially helpful for constrained fuzzy classification problems. In particular, the model allows for prescribed average percentages of each class in predictions. Numerical illustrations are provided for both simulated and real data and show the importance of the constraint on predicted values. The method also competes with the 69 other models of an open real-world benchmark.