This paper draws upon the scholarship of interdisciplinarity to argue that Economics, like all disciplines, should be open to a wide range of theories and methods, and the study of all relevant phenomena. A classification of the different methods and theory types used by scholars identifies key strengths and weaknesses of each. Different schools of heterodox [that is, non-neoclassical] economics, as well as neoclassical economics itself, emphasize different sets of theory and method. Each thus has a unique contribution to make to a holistic understanding of the economy. At present, different heterodox schools, like neoclassical economics itself, tend to act as if it were thought that their theory and method were superior. This paper urges a quite different attitude: different heterodox schools, as well as neoclassical economics, should be seen as complements rather than substitutes. That is, the insights of different schools of thought within Economics can and should be integrated just as disciplinary insights are integrated within interdisciplinary scholarship. The classification also identifies valuable theory types not presently embraced by any heterodox approach. Heterodoxy needs also to embrace the causal linkages between economic and diverse non-economic phenomena; the paper outlines a strategy for organizing the complex understandings that emerge from such a project. Some might recoil at the complexity of an academic enterprise that embraces such a wide range of phenomena, theory, and method; this paper shows how these diverse investigations can be organized in terms of the classifications presented such that all economists could readily appreciate the contributions of others. The paper also makes suggestions regarding the daily practice of heterodox economists, and draws lessons for heterodoxy from interdisciplinary research practice.