Artificial Intelligence systems are increasingly deployed in settings where ensuring robustness, fairness, or domain-specific properties is essential for regulation compliance and alignment with human values. However, especially on Neural Networks, property enforcement is very challenging, and existing methods are limited to specific constraints or local properties (defined around datapoints), or fail to provide full guarantees. We tackle these limitations by extending SMiLE, a recently proposed enforcement framework for NNs, to support global relational properties (defined over the entire input space). The proposed approach scales well with model complexity, accommodates general properties and backbones, and provides full satisfaction guarantees. We evaluate SMiLE on monotonicity, global robustness, and individual fairness, on synthetic and real data, for regression and classification tasks. Our approach is competitive with property-specific baselines in terms of accuracy and runtime, and strictly superior in terms of generality and level of guarantees. Overall, our results emphasize the potential of the SMiLE framework as a platform for future research and applications.