Building on the recent discovery of tough nanocrystalline Cu-Zr alloys with amorphous intergranular films, this paper investigates ternary nanocrystalline Cu-Zr-Hf alloys with a focus on understanding how alloy composition affects the formation of disordered complexions. Binary Cu-Zr and Cu-Hf alloys with similar initial grain sizes were also fabricated for comparison. The thermal stability of the nanocrystalline alloys was evaluated by annealing at 950 °C (>95% of the solidus temperatures), followed by detailed characterization of the grain boundary structure. All of the ternary alloys exhibited exceptional thermal stability comparable to that of the binary Cu-Zr alloy, and remained nanocrystalline even after two weeks of annealing at this extremely high temperature. Despite carbide formation and growth in these alloys during milling and annealing, the thermal stability of the ternary alloys is mainly attributed to the formation of thick amorphous intergranular films at high temperatures. Our results show that ternary alloy compositions have thicker boundary films compared to the binary alloys with similar global dopant concentrations. While it is not required for amorphous complexion formation, this work shows that having at least three elements present at the interface can lead to thicker grain boundary films, which is expected to maximize the previously reported toughening effect.