Ternary III−V nanowires are commonly grown using the Au-seeded vapor−liquid−solid method, wherein the solid nanowires are grown from nanoscale liquid seed particles, which are supplied with growth species from the surrounding vapor phase. A result of the small size of these seed particles is that their composition can vary significantly during the cyclical layer-by-layer growth, despite experiencing a constant pressure of growth species from the surrounding vapor phase. Variations in the seed particle composition can greatly affect the solid nanowire composition, and these cyclical dynamics are poorly understood for ternary nanowire growth. Here, we present a method for simulating nanowire growth which captures the complex cyclical dynamics using a kinetic Monte Carlo framework. In the framework, a nanowire grows through the attachment or detachment of one III−V pair at the time, with rates that are based on the momentary composition of the seed particle. The composition of the seed evolves through the attachment and detachment of III−V pairs to the solid nanowire and through the impingement or evaporation of single atoms to the surrounding vapor. Here, we implement this framework using the As−Au−Ga−In materials system and use it to simulate the growth of Auseeded InGaAs nanowires with an average solid Ga/III ratio around 0.5. The results show that nucleation preferentially occurs via clusters of InAs and that the compositional hierarchy of the liquid seed (X As < X Ga < X In ) determines much of the dynamics of the system. We see that imposing a constraint on the simulation, that only the most recently attached III−V pair can be detached, resulted in a significant narrowing of the compositional profile of the nanowire. In addition, our results suggest that, for ternary systems where the two binaries are heavily mismatched, the dynamics of the seed particle may result in an oscillating compositional profile.