Because of the prohibitive scaling of ab initio techniques for modeling chemical species with high accuracy, they are not generally tractable for large systems. It is therefore of considerable interest to develop high-accuracy computational models with low computational cost that can afford predictions of electronic structure and properties of macromolecular species. Composite methods, as first introduced by Pople [Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys.1989, 90, 5622.], are an intuitive solution to this problem as they seek to systematically increase accuracy in model chemistries by taking advantage of favorable error cancellation among reasonably low-cost models. By linearly combining a series of carefully chosen model chemistries, the result of a prohibitive-scaling correlated model chemistry with a large basis set may be approximated with relatively good fidelity. However, the full extent to which the choice of low-cost models dictates the predictive accuracy of composite methods is not known, and a full exploration of all model chemistries would be advantageous for the design and validation of a generalizable composite method for widespread application. Here, we show that remarkable accuracy can be generally achieved with composite methods that are more judiciously constructed, leading to increased accuracy with significantly reduced computational cost. By designing a systematic procedure for the automated generation and assessment of over 10 billion unique composite methods, we have extensively explored the space of modern model chemistries to elucidate important design principles in the construction of reliable composite procedures. We anticipate our work to be the starting point in the pursuit of creative approaches to modeling large chemical systems with high accuracy by using novel combinatorial modeling.