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We investigate the coarsening dynamics of the three-phase eutectic Al-Ag2Al-Al2Cu at 723 K via in situ transmission X-ray nano-tomography. Unlike previous investigations that compared observations between different samples annealed for different times, our three-dimensional measurement shows at nanoscale resolution the microstructural changes occurring in the same field-of-view, enabling new insight on the capillary-driven evolution of a ladder-like pattern. With the aid of a new reconstruction algorithm and machine learning segmentation, we trace the interfaces of the eutectic and observe significant structural changes within 4 hr. of aging. Even though the average length-scales of the eutectic solids follow a temporal power law, the microstructure is not self-similar. Instead, it evolves (in part) through the coalescence of neighboring Ag2Al solids at the expense of the intervening Al2Cu. By combining our X-ray data with electron diffraction to identify the common planes at the interphase boundaries, we show that coalescence leads to a decrease in lattice misfit, and hence, interfacial energy. At longer times, the interphase boundaries with low misfit compete for surface area, resulting in a ‘locking’ of the interfacial shape.