prevalent. This standard readout scheme has significant drawbacks: in addition to the Purcell effect, it suffers from a limitation on the maximal number of photons in the readout mode, which restricts the signal-to-noise ratio (SNR) and the Quantum Non-Demolition (QND) nature of the readout. Here, we explore the high-power regime by engineering a nonlinear coupling between a transmon qubit and its readout mode. Our approach builds upon previous work by Dassonneville et al. [Physical Review X 10, 011045 (2020)], on qubit readout with a non-perturbative cross-Kerr coupling in a transmon molecule. We demonstrate a readout fidelity of 99.21% with 89 photons utilizing a parametric amplifier. At this elevated photon number, the QND nature remains high at 96.7%. Even with up to 300 photons, the QNDness is only reduced by a few percent. This is qualitatively explained by deriving a critical number of photons associated to the nonlinear coupling, yielding a theoretical value of n¯critr=377 photons for our sample’s parameters. These results highlight the promising performance of the transmon molecule in the high-power regime for high-fidelity qubit readout.