Alloys based on γ-aluminide are a promising class of heat-resistant materials for the manufacture of parts of modern aircraft engines, the maximum operating temperature of which is in the range of 600–700°C. The main advantages of these alloys are the combination of low density, high structural stability, and heat resistance. However, due to the natural characteristics of intermetallic compounds (structure ordering, strong covalent bonding), γ-alloys are characterized by low plasticity compared to traditional titanium alloys that complicates the industrial application of these alloys and increases the complexity of the process of manufacturing semi-finished products and final parts. For the successful use of γ-alloys and their introduction into modern aircraft engines, it is necessary to increase their technological plasticity, while ensuring high strength and heat resistance characteristics. One of the most effective ways to accomplish this task is by means of alloying and modification. The work considers the influence of alloying elements niobium and molybdenum, as well as the modifying element rhenium, on the morphology, phase composition and mechanical characteristics of the γ-alloy in the Ti–Al system. The optimal concentrations of the elements Nb, Mo and Re in the titanium aluminide-based Ti–29Al–7Nb–2Mo alloy are determined, ensuring a two-fold increase in the mechanical properties of the alloy due to the weakening of covalent bonding forces. Using the method of high-temperature thermal analysis, it is established that the introduction of niobium, molybdenum and rhenium into the intermetallic does not change the sequence of transformations and the temperature ranges of phase-regions existence.