The Cu–Ti–Zr system and associated multicomponent systems are of practical interest as their alloys show high bulk glass forming ability. The Cu–Ti–Zr system is divided into two independent subsystems (Ti–CuTi2–CuZr2–Zr and Cu–CuTi2–CuZr) by the quasibinary vertical CuTi2–CuZr2 section. In this paper, phase equilibria in the Ti–CuTi2–CuZr2–Zr subsystem were experimentally studied. The structure of the as-cast binary and ternary alloys and the temperature of phase transformations in the samples that were cast and annealed at 750°C were studied by physicochemical analysis methods. The results were used to construct the liquidus and solidus surfaces, phase diagram, and vertical sections with 10, 20, and 30 at.% Cu, confirm the congruent formation of binary CuTi2 and CuZr2 compounds at 1012 and 1000°C, and find the composition and temperature of invariant eutectic reactions with their participation. The liquidus surface consists of two primary crystallization surfaces of infinite series of (βTi, βZr) (β) and Cu (Ti, Zr)2 (γ) phases, which intersect along the univariant eutectic curve. The liquidus temperatures decrease from the boundary binary systems to the ternary one, reaching the minimum at 845 °C. The solidus surface is characterized by the coexistence of the β and γ phases (β + γ range) over the entire composition range. The copper solubility is from 5 to 8 at.% in the β phase and up to 2 at.% in the γ phase. This two-phase region is formed through the eutectic L ⇄ (βTi, βZr) + Cu (Ti, Zr)2 reaction. There is also a minimum at 845°C on the solidus surface. The compositions of the two solid and one liquid phases coexisting at the minimum temperature are found on a single tie-line, along which the three-phase equilibrium is invariant. The compositions of the phases in this equilibrium are as follows: Lmin—Cu30Ti37Zr33, βmin—Cu10.5Ti62Zr28.5, and γmin—Cu32Ti35Zr33 (at.%). According to differential thermal analysis, the minimum temperature of the eutectoid (βTi, βZr) ⇄ (αTi, αZr) + Cu(Ti,Zr)2 transformation is 570°C.