A method of operating a combustor of a turbomachine on a total fuel input that contains a concentration of hydrogen that is greater than about 80% is provided. The method includes injecting a first mixture of air and a first fuel containing a first amount of hydrogen into the primary combustion zone of the combustor to generate a first flow of combustion gases having a first temperature. The method further includes injecting, with one or more premix injectors disposed downstream of the fuel nozzles, a second mixture of air and a second fuel containing a second amount of hydrogen into the secondary combustion zone of the combustor to generate a second flow of combustion gases having a second temperature. The method further includes separately injecting a third fuel into secondary combustion zone to generate a third flow of combustion gases having a third temperature.