Transition metal trialuminides of the Al3X type of groups 4 and 5 of the periodic system have reduced density, high melting points, and corrosion resistance. Aluminides with a cubic lattice of the Al3Sc type can be used as a nucleating phase for aluminum alloys. However, low plasticity and a tetragonal lattice limit their application. In this work, we stabilized the metastable cubic lattice of Al3X-type aluminides by replacing aluminum with copper. The conditions for the formation of L12 metastable aluminides in the Al–Cu–TM (TM: Ti, Zr, Hf) alloys were studied using a wide range of copper concentrations. A high concentration of copper (hypereutectic alloys) is the one of the necessary conditions for the formation of (Al1−xCux)3Ti, (Al1−xCux)3Zr, (Al1−xCux)3Hf aluminides. With an increase in the copper concentration, the number of metastable aluminides sharply increased. The process of their formation strongly depended on the sequence of dissolution of the corresponding components in the melts. The low volume fraction of precipitated titanium aluminides was the result of insufficient supersaturation of α-Al with titanium (at the peritectic temperature) compared to that for alloys with zirconium and hafnium. Under identical synthesis conditions in the crystal lattice of metastable aluminides formed in experimental Al–Cu–Ti, Al–Cu–Zr, Al–Cu–Hf alloys, copper was found to substitute up to 8, 10, and 13 at.% of aluminum, respectively. The crystallographic and dimensional similarities of the lattices in metastable transition metal aluminides and in α-Al suggest their usefulness as modifying additions in aluminum-based alloys.