Composition of ternary III-V nanowires became a subject of recent intensive studies inspired by several optoelectronic applications. Among these nanostructures, phosphide nanowires possess a wider bandgap making it especially promising for applications operating in the green visible range. However, unlike other III-V materials, the growth of AlGaP nanowires remains rather unexplored. In this work, we model the stationary composition of self-catalyzed AlGaP grown by molecular beam epitaxy. We show that under a wide range of growth parameters our theoretical approach does not require any fitting parameter and thus allows direct interpretation of experimental data. The obtained numerical results demonstrate a tendency to Al domination over Ga at rather low fluxes of the first. Interesting phenomena of the rise of Al fraction with an increase of the total group III flux is demonstrated. On the other hand, high tolerance of the chemical composition to the temperature, concentration of phosphorus in the droplet, and adatom kinetics is shown numerically.