Heterogeneous multiprocessor systems have increased in complexity to provide both high performance and energy efficiency for a diverse range of applications. This motivates the need for a standard framework that enables the management, at runtime, of software applications executing on these processors. This paper proposes the first fully application- and platform-agnostic framework for runtime management approaches that control and optimise software applications and hardware resources. This is achieved by separating the system into three distinct layers connected by an API and cross-layer constructs called knobs and monitors. The proposed framework also supports the management of applications that are executing concurrently on heterogeneous platforms. The operation of the proposed framework is experimentally validated using a basic runtime controller and two heterogeneous platforms, to show how it is application- and platform-agnostic and easy to use. Furthermore, the management of concurrently executing applications through the framework is demonstrated. Finally, two recently reported runtime management approaches are implemented to demonstrate how the framework enables their operation and comparison. The energy and latency overheads introduced by the framework have been quantified and an open-source implementation has been released.