  In this work we provide an exact and efficient numerical approach to simulate
multi-time correlation functions in the Mahan-Nozi\`{e}res-De Dominicis model,
which crudely mimics the spectral properties of doped two-dimensional
semiconductors such as monolayer transition metal dichalcogenides. We apply
this approach to study the coherent two-dimensional electronic spectra of the
model. We show that several experimentally observed phenomena, such as peak
asymmetry and coherent oscillations in the waiting-time dependence of the
trion-exciton cross peaks of the two-dimensional rephasing spectrum, emerge
naturally in our approach. Additional features are also present which find no
correspondence with experimentally expected behavior. We trace these features
to the infinite hole mass property of the model. We use this understanding to
construct an efficient approach which filters out configurations associated
with the lack of exciton recoil, enabling the connection to previous work and
providing a route to the construction of realistic two-dimensional spectra over
a broad doping range in two-dimensional semiconductors.
