Oligomerization plays an important role in the function of many proteins. Thus, understanding, predicting, and, ultimately, engineering oligomerization presents a long-standing interest. From the perspective of structural biology, protein-protein interactions have mainly been analyzed in terms of the biophysical nature and evolution of protein interfaces. Here, our aim is to quantify the importance of the larger structural context of protein interfaces in protein interaction evolution. Specifically, we ask to what extent intersubunit geometry affects oligomerization state. We define a set of structural parameters describing the overall geometry and relative positions of interfaces of homomeric complexes with different oligomeric states. This allows us to quantify the contribution of direct sequence changes in interfaces versus indirect changes outside the interface that affect intersubunit geometry. We find that such indirect, or allosteric mutations affecting intersubunit geometry via indirect mechanisms are as important as interface sequence changes for evolution of oligomeric states.