Building on previous studies of invariant ternary eutectic Al-Al2Cu-Al2CuMg, this work aims to deepen our understanding of the microstructural possibilities in the Al-rich region of the Al-Cu-Mg phase diagram by considering the solidification behaviour of several off-eutectic compositions. Four Al-Cu-Mg alloys were directionally solidified at a constant growth rate (1.25 μm/s) and thermal gradient (9-14 K/mm) using a Bridgman-type furnace and analysed using a combination of scanning electron microscopy, energy-dispersive X-ray spectroscopy, X-ray diffraction, and differential scanning calorimetry. Qualitative and quantitative analyses showed a preference for faceted Al2Cu dendrites surrounded by a ternary eutectic matrix in the two Mg-poor samples, even though one composition was not in the primary Al2Cu phase region. The two Al-poor samples consisted of large regions of three different intermetallic phases and little eutectic, making these samples very brittle.