Counterfactual explanations have been proposed to provide actionable insights for competitive black-box classifiers by suggesting modifications to alter undesirable prediction outcomes into desired ones. Despite the rapid development of counterfactual methods that provide insightful “what-if” explanations in various applications, most existing approaches fail to generate counterfactuals considering whether the contextual integrity of the original instance –such as demographic consistency or user-specific constraints– is explicitly controlled. This article introduces Context-Aware Counterfactual Explanations (CACTUS), a novel framework for generating feasible counterfactuals that can either preserve or change the user-defined contextual features of the original instance. We illustrate CACTUS by conducting the counterfactual search in a context-conditional latent space, using a composite β-VAE model that can learn enhanced disentanglement of context-related factors. Our experimental evaluation indicates that the context-preserving CACTUS outperforms state-of-the-art methods in maintaining contextual consistency, while remaining competitive in compactness, proximity, and validity metrics. Moreover, our qualitative analysis highlights that CACTUS generates plausible counterfactual explanations that can explicitly preserve or modify user-defined contexts in real-world scenarios.