The ability to design multi-resonant thermal emitters is essential to the advancement of a wide variety of applications, including thermal management and sensing. These fields would greatly benefit from the development of more efficient tools for predicting the spectral response of coupled, multi-resonator systems. In this work, we propose a semi-analytical prediction tool based on coupled-mode theory. In our approach, a complex thermal emitter is fully described by a set of coupled-mode parameters, which can be straightforwardly calculated from simulations of unit cells containing single and double resonators. We demonstrate the accuracy of our method by predicting and optimizing spectral response in a coupled, multi-resonant system based on hBN ribbons. The approach described here can greatly reduce the computational overhead associated with spectral design tasks in coupled, multi-resonant systems.