Despite the growing collection and use of private data in the cloud, there remains a fundamental disconnect between unified data governance and the storage system enforcement techniques. On one side, high-level governance policies derived from regulations like General Data Protection Regulation (GDPR) have emerged with stricter rules dictating who, when and how data can be processed. On the other side, storage-level controls, both role- or attribute-based, continue to focus on access/deny enforcement. In this paper, we propose how to bridge this gap. We introduce Deep Enforcement, a system that provides unified governance and transformation policies coupled with data transformations embedded into the storage fabric to achieve policy compliance. Data transformations can vary in complexity, from simple redactions to complex differential privacy-based techniques to provide the required amount of anonymization. We show how this architecture can be implemented into two broad classes of data storage systems in the cloud: object storages and SQL databases. Depending on the complexity of the transformation, we also demonstrate how to implement them either in-line (on data access) or off-line (creating an alternate cached dataset).