Personal Data Management Systems (PDMSs) arrive at a rapid pace providing individuals with appropriate tools to collect, manage and share their personal data. At the same time, the emergence of Trusted Execution Environments (TEEs) opens new perspectives in solving the critical and conflicting challenge of securing users' data while enabling a rich ecosystem of data-driven applications. In this paper, we propose a PDMS architecture leveraging TEEs as a basis for security. Unlike existing solutions, our architecture allows for data processing extensiveness through the integration of any userdefined functions, albeit untrusted by the data owner. In this context, we focus on aggregate computations of large sets of database objects and provide a first study to mitigate the very large potential data leakage. We introduce the necessary security building blocks and show that an upper bound on data leakage can be guaranteed to the PDMS user. We then propose practical evaluation strategies ensuring that the potential data leakage remains minimal with a reasonable performance overhead. Finally, we validate our proposal with an Intel SGX-based PDMS implementation on real data sets.