The Jaynes–Cummings (JC) model has been the theoretical workhorse for understanding cavity quantum electrodynamics (QED) and for exploring multiphoton effects caused by the quantization of light. Today, it is an indispensable tool used to describe a variety of quantum optical systems, including semiconductor quantum-dot (QD) cavities, atoms in cavities, and superconducting circuits. Unfortunately, dissipation in many cavity-QED systems, especially QD structures, can strongly inhibit any direct spectral features of higher lying photon states and their spectral anharmonicities. In this work, we introduce a strategy to directly access and probe these multiphoton states and show that they can be directly observed even in the presence of a significant amount of dissipation. Our excitation scheme employs off-resonant excitation of a coupled QD cavity system using a nonlinear coherent drive, and the computed fluorescence spectra demonstrate the feasibility of the direct spectroscopic observation of higher rungs of the JC ladder using realistic QD cavity systems.