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Cobalt-based alloys with nickel and titanium represent a promising class of materials for the development of novel amorphous and high-temperature-resistant alloys. The targeted design of such materials requires detailed knowledge of the thermodynamic properties of liquid alloys. In this work, high-temperature calorimetry was employed to investigate the partial enthalpy of mixing of titanium in the Co–Ni–Ti liquid alloys along the cross-sections x Co / x Ni = 3, x Co / x Ni = 1/3, and x Co / x Ni = 1 at 1873 K and in the concentration range x Ti = 0–0.6. The partial mixing enthalpy of titanium exhibits negative values, indicating strong interatomic interactions among the components in the melt. The integral mixing enthalpy Δ m H over the entire compositional triangle was described using the Redlich–Kister–Muggianu formalism. The Δ m H function shows pronounced negative values, emphasizing the significant role of CoTi and NiTi binary interactions. The associate solution model (ASM) was applied to describe the temperature and composition dependence of the thermodynamic mixing functions in the liquid Co–Ni–Ti alloys. The integral enthalpy Δ m H , excess entropy Δ m S ex , excess Gibbs energy Δ m G ex , and Gibbs energy Δ m G of mixing were evaluated in the temperature range 800–1873 K. It was shown that these thermodynamic functions exhibit increasing negative deviations from ideality upon cooling of the melts. Within the ASM framework, the degree of chemical short-range order in the Co–Ni–Ti liquid alloys was assessed as the total mole fraction of associates Σ x assoc in the solution. It was demonstrated that the Σ x assoc is significant and increases with decreasing temperature. The amorphization composition range for the Co–Ni–Ti liquid alloys was predicted based on our previously proposed empirical criterion related with Σ x assoc . The predicted range of x Ti ≈ 0.2–0.8 is in satisfactory agreement with known compositions of amorphous alloys in the edged binary systems.