Post-Kohn--Sham methods are used to evaluate the ground-state correlation energy and the orbital self-energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random-phase approximation and the multicomponent Green's function GW approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn--Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, the GW quasiparticle energies are needed to study light-matter interactions with the Bethe--Salpeter equation.