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In this Article, we explore how the chemical pressure (CP) features of an intermetallic phase may provide opportunities to couple perturbations in electron count with the stabilization of the underlying geometrical structure. AuCu3‐type LnGa3 (Ln = lanthanide or group 3 metal) phases contain octahedral cavities of negative CP held open by overly compressed Ln–Ga interactions, leading to a series of transition metal‐stuffed derivatives. We present new additions to this family with the synthesis and crystal structures of Dy4T1−xGa12 with (T, x) = (Ag, 0.29) and (Ir, 0.15), adopting Y4PdGa12‐type superstructures of the AuCu3‐type. Density Functional Theory (DFT)‐CP calculations, when adjusted to avoid dipolar CP features, affirm that T atom incorporation provides a mechanism for the relief of packing tensions, while electronic density of states distributions illustrate that the T atoms serve largely as electron or hole donors to the band structure, as needed for them to attain d10 configurations. The maximum obtainable value for x may be limited by a mismatch between the Fermi energy and pseudogap, in line with the balance of factors envisioned by the frustrated and allowed structural transitions principle. Trends in resistivity measurements on T = Ir, Pd, and Ag compounds are interpretable in terms of the varying degrees of disorder arising from x< 1.0.