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Conventionally, high-throughput computational materials searches start from an input set of bulk compounds extracted from material databases, and this set is screened for candidate materials for specific applications. In contrast, many functional materials, and especially semiconductors, are heavily engineered alloys or solid solutions of multiple compounds rather than a single bulk compound. To improve our ability to design functional materials, in this work we propose a framework and open-source code to automatically construct possible "alloy pairs" and "alloy systems" and detect "alloy members" from a set of existing, experimental or calculated ordered compounds, without requiring any additional metadata beyond their crystal structure. We provide analysis tools to estimate stability across each alloy. As a demonstration, we apply this framework to all inorganic materials in the Materials Project database to create a new database of over 600,000 unique alloy pair entries that can then be used in materials discovery studies to search for materials with tunable properties. This new database has been incorporated into the Materials Project website and linked with corresponding material identifiers for any user to query and explore. Using an example of screening for p-type transparent conducting materials, we demonstrate how using this methodology reveals candidate material systems that might otherwise have been excluded by a traditional screening. This work lays a foundation from which materials databases can go beyond stoichiometric compounds, and approach a more realistic description of compositionally tunable materials.