Abstract Gas turbines featuring sequential combustion architectures are ideally suited to deliver CO2-free, fuel-flexible, and on-demand power to the grid. A sequential combustor is comprised of two axially staged flames. Typically, the first stage is a swirl-stabilized propagating flame. The hot products of the first stage are diluted with air before additional fuel is injected in the second stage. The resulting vitiated mixture leads to auto-ignition in the second combustor. The sequential architecture can be leveraged to vary the fuel split between the combustion chambers to account for different reactivities of alternative fuels. Thermoacoustically stable combustors are critical to ensure low emissions, high reliability, and mechanical integrity. Under specific off-design conditions, the auto-ignition-stabilized second stage can be subject to transversal instabilities. This article presents a finite-element-coupled method to model the thermoacoustic behavior of the Ansaldo Energia H-class GT36 reheat combustion stage in a very cost-effective manner. To do so, the auto-ignition flame is divided into multiple parts for which the flame transfer function (FTF) methodology commonly used for planar waves is applied. The stability of transverse eigenmodes is assessed and validated against experiments performed under engine conditions. We show that the framework can correctly predict the stability of high-frequency combustor modes. Consequently, it can be used to get reliable stability estimates of high-frequency thermoacoustic modes in industrial reheat combustion chambers and to ensure that such instabilities are avoided.