Composable many-core systems enable the independent development and analysis of applications which will be executed on a shared platform where the mix of concurrently executed applications may change dynamically at run time. For each individual application, an off-line Design Space Exploration (DSE) is performed to compute several mapping alternatives on the platform, offering Pareto-optimal trade-offs in terms of real-time guarantees, resource usage, etc. At run time, one mapping is then chosen to launch the application on demand. In this context, to enable an independent analysis of each individual application at design time, so-called inter-application isolation schemes are applied which specify temporal or spatial isolation policies between applications. S.o.t.a. composable many-core systems are developed based on a fixed isolation scheme that is exclusively applied to every resource in every mapping of every application and use a timing analysis tailored to that isolation scheme to derive timing guarantees for each mapping. A fixed isolation scheme, however, heavily restricts the explored space of solutions and can, therefore, lead to suboptimality. Lifting this restriction necessitates a timing analysis that is applicable to mappings with an arbitrary mix of isolation schemes on different resources. To address this issue, we present an isolation-aware timing analysis that unlike existing analyses can handle multiple isolation schemes in combination within one mapping and delivers safe yet tight timing bounds by identifying and excluding interference scenarios that can never happen under the given combination of isolation schemes. Based on the timing analysis, we present a DSE which explores the choices of isolation scheme per resource within each mapping. Experimental results demonstrate the advantage of the proposed approach over approaches based on a fixed isolation scheme.