Design space exploration (DSE) is a key activity in embedded system design methodologies and can be supported by well-defined models of computation (MoCs) and predictable platform architectures. The original design model, covering the application models, platform models and design constraints needs to be converted into a form analyzable by computer-aided decision procedures such as mathematical programming or genetic algorithms. This conversion is the process of design space identification (DSI), which becomes very challenging if the design domain comprises several MoCs and platforms. For a systematic solution to this problem, separation of concerns between the design domain and decision domain is of key importance. We propose in this paper a systematic DSI scheme that is (a) composable, as it enables the stepwise and simultaneous extension of both design and decision domain, and (b) tuneable, because it also enables different DSE solving techniques given the same design model. We exemplify this DSI scheme by an illustrative example that demonstrates the mechanisms for composition and tuning. Additionally, we show how different compositions can lead to the same decision model as an important property of this DSI scheme.