Thermodynamic modelling of the multi-component system from the low-order subsystems in a self-consistent way and a quantitative description of the uncertainty in the modelling are critical to multicomponent alloy design. The Ag–Cu, Ag–Co, and Co–Cu binary systems are the subsystems to build the Ag–Cu–Co ternary system. They are important for the Ag–Cu-based lead-free solders and represent typical eutectic, monotectic, and peritectic systems. In this work, we present a case study of modelling and uncertainty quantification with the recently developed Extensible Self-optimizing Phase Equilibria Infrastructure (ESPEI). Enthalpies of mixing at 0 K were calculated by density functional theory (DFT)-based first-principles method using the special quasi-random structures (SQS) to compensate for the lack of thermochemical solid solution data. Incorporating the collected experimental data, the three sub-binary systems were successfully assessed, and the Ag–Cu–Co ternary system was subsequently modelled. The calculated phase diagrams of the ternary system and the sub-binary system agree with the experiments well. The reliability of the obtained models was further validated by the “residual driving force” approach. The probability distribution of the mono-variant points reside within composition-temperature space is also determined by the Phase Diagram Uncertainty Quantification (PDUQ) tool, providing confidence measures in the design of solder alloys.