While elemental substitution is the most common way of tuning properties in solid state compounds, this approach can break down in fantastic ways when the stability range of a structure type is exceeded. In this article, we apply the Frustrated and Allowed Structural Transitions (FAST) principle to understand how structural complexity, in this case incommensurate modulations, can emerge at the composition limits of one common intermetallic framework, the BaAl4 type. While the Dy-Ga binary intermetallic system contains no phases related to the BaAl4 archetype, adding Cu to form a ternary system creates a composition region that is rich in such phases, induding some whose structures remain unknown. We begin with an analysis of electronic and atomic packing issues faced by the hypothetical BaAl4-type phase DyGa4 and a La3Al11-type variant (in which a fraction of Ga t pairs are substituted by single Ga atoms). Through an inspection of its electronic density of states (DOS) distribution and DFT-Chemical Pressure (CP) scheme, we see that the stability of BaAl4-type DyGa4 is limited by an excess of electrons and overly large coordination environments around the Dy atoms, with the latter factor being particularly limiting. The inclusion of Cu into the system is anticipated to soothe both issues through the lowering of the valence electron count and the release of positive CPs between atoms surrounding the Dy atoms. With this picture in mind, we then move to an experimental investigation of the Dy-Cu-Ga system, elucidating the structure of Dy(Cu0.18Ga0.82)(3.71(1)). In this compound, the BaAl4 type is subject to a 2D incommensurate modulation (q(1) = 0.31a* + 0.2b*, q(2) = 0.31a* - 0.2b*), which can be modeled in the (3+2)D superspace group Pmmm(alpha beta 0)000(alpha-beta 0)000. The resulting structure solution contains blocks of the La(3)Al(11 )type, with the corners of these domains serving to shrink the Dy coordination environments. These results highlight how the addition of a well-chosen third element to a binary system with a missing-but plausible-compound (BaAl4-type DyGa4) can bring it to the cusp of stability with intriguing structural consequences.