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The linewidth of excitonic complexes provides direct insights into the nature of optical excitations in materials and their decay pathways. In doped semiconducting monolayers of transition metal dichalcogenides (TMDs), the linewidth associated with an exciton resonance is sensitive to extra charge carriers due to the nontrivial dielectric screening from the Fermi sea and the variety of states an exciton can scatter to, even in the weak-doping limit. Therefore, computational approaches and first-principles calculations can provide unique insights into the microscopic origin of such interactions and the nature of the associated scattering events. In this talk, we present results from first-principles calculations of Dyson-like equations associated with 3- and 4-body interacting particle problems (involving electrons and holes) to address this problem. We compare our results with perturbative calculations based on the scattering of excitons to Fermi-sea electron-hole pairs and assess the importance of many-body screening, band-filling effects, and the ab initio description of electron-hole coupling terms.