Titanium and its alloys are becoming more and more popular for additive manufacturing and especially for structural light-weighting due to their good mechanical properties in terms of low density. That is the reason why the development of new titanium alloys is becoming more and more an essential topic. In the present work, the effects of ternary added alloying elements on the Ti-6.4(wt.%)Ni eutectoid system are investigated. The aim is to achieve a high specific Young's modulus and high specific stiffness, thus making the alloys attractive for lightweight construction in the aerospace industry. This can be achieved by tailored adjustment of intermetallic phases through heat treatments. For this purpose, the behavior of the titanium-nickel eutectoid system is primarily considered by adding sluggish eutectoids, such as iron and chromium. While Ni is one of the active eutectoid forming elements and shows a fast transformation behavior. In addition, the influence of the addition of alpha-stabilizing aluminum and of the neutral element lanthanum is also investigated. Thermodynamic calculations and thermal analyses such as dilatometry and differential scanning calorimetry supported by microstructural analyses such as scanning electron microscopy and X-ray diffraction are performed to gain insight into the phase transformations that occur. In addition, specific mechanical properties such as microhardness, specific Young's modulus via ultrasonics, specific stiffness and the behavior in compression tests are determined. In the course of the investigations, it was found that considerable microhardness increase could be obtained in the ternary alloys Ti-6.4Ni-2Fe and Ti-6.4Ni-2Cr by solution annealing and aging above the eutectoid temperature or beta-transus temperature due to formation of intermetallic phases or an ordered variant of the beta-phases, but the plasticity of the materials became unusable due to the omega phase occurring. When ageing below the beta-starting temperature, the brittleness of the materials could be lowered and the specific stiffness increased into an acceptable range. Furthermore, spinodal decomposition of the alpha phases of all alloys after direct-aging was detected. Further investigations need to clarify whether these ternary systems (Ti-6.4Ni-2Cr and Ti-6.4Ni-2Fe) can be formed into a wire by powder extrusion in order to perform first welding tests. After homogenization and aging, the alloy Ti-6.4Ni-9Al showed attractive microhardness values for further tests. Last but not least, limited solubility of lanthanum in the Ti-Ni system depending on the Ni content was observed in the microstructure analyses.