Multi-Processor Systems on a Chip (MPSoCs) are suitable platforms for the implementation of complex embedded applications. An MPSoC is composable if the functional and temporal behaviour of each application is independent of the absence or presence of other applications. Composability is required for application design and analysis in isolation, and integration with linear effort. In this paper we propose a composable organisation for the top level of a memory hierarchy. This organisation preserves the short (one cycle) access time desirable for a processor's frequent local accesses and enables the predictability demanded by real-time applications. We partition the local memory in two blocks, one private, for local tile data, and another sh...