Single crystal nickel-based superalloys are used in modern gas turbines because of their remarkable resistance to creep deformation at elevated temperatures, which is ensured by the addition of significant amounts of refractory elements. Too high concentrations of refractory elements can lead to the formation of topologically-close packed (TCP) phases during exposure to conditions of high temperature and stress which result in the degradation of the creep properties. The traditional methods for predicting the occurrence of TCP phases in Ni-based superalloys have been based on the PHACOMP and newPHACOMP methodologies which are well-known to fail with respect to new generations of alloys. In this work a novel two-dimensional structure map (Nbar, deltaV/V) for TCP phases where Nbar is the valence-electron count and deltaV/V is a compositional dependent size factor. This map is found to separate the experimental data on the TCP phases of binary, ternary and multi-component TCP phases into well-defined regions corresponding to different structure types such as A15, sigma, chi, delta, P, R, mu, and Laves. In particular, increasing size factor separates the A15, sigma and chi phases from the delta, P, R, mu phases. The structure map is then also used in conjunction with CALPHAD computations of sigma phase stability to show that the predictive power of newPHACOMP for the seven component Ni–Co–Cr–Ta–W–Re–Al system is indeed poor. In order to gain a microscopic understanding of the observed structural trends, namely the differences between the two groups of TCP structures with increasing deltaV/V and the trend from A15 to sigma to chi with increasing Nbar, the electronic structure is coarse-grained from density functional theory (DFT) to tight-binding to bond-order potentials (BOPs). First, DFT is used to calculate the structural energy differences across the elemental 4d and 5d transition metal series and the heats of formation of the binary alloys Mo-Re, Mo-Ru, Nb-Re, and Nb-Ru. These calculations show that the valence electron concentration stabilizes A15, sigma and chi but destablizes mu and Laves phases. The latter are shown to be stabilized instead by relative size difference. Second, a simple canonical TB model and in combination with the structural energy difference theorem is found to qualitatively reproduce the energy differences predicted by the elemental DFT calculations. The structural energy difference theorem rationalizes the importance of the size factor for the stability of the mu and Laves binary phases as observed in the structure map and DFT heats of formation. Finally, analytic BOP theory, is employed to identify the structural origins of the energetic differences between TCP structure-types that lead to the trends found within the two-dimensional structure map.