The present disclosure is directed to a method of operating a gas turbine engine with an interdigitated turbine section. The engine includes a fan rotor, an intermediate pressure compressor, a high pressure compressor, a combustion section, and a turbine section in serial flow arrangement. The turbine section includes, in serial flow arrangement, a first stage of a low speed turbine rotor, a high speed turbine rotor, a second stage of the low speed turbine rotor, an intermediate speed turbine rotor, and one or more additional stages of the low speed turbine rotor. The low speed turbine rotor is coupled to the fan rotor via a low pressure shaft. The intermediate speed turbine rotor is coupled to the intermediate pressure compressor via an intermediate pressure shaft. The high speed turbine rotor is coupled to the high pressure compressor via a high pressure shaft. The method includes rotating the low speed turbine rotor in a first direction along the circumferential direction; rotating the high speed turbine rotor in a second direction opposite of the first direction along the circumferential direction; and rotating the intermediate speed turbine rotor in the second direction.