A compound engine assembly with an engine core including at least one internal combustion engine, a compressor, and a turbine section where the turbine shaft is configured to compound power with the engine shaft. The turbine section may include a first stage turbine and a second stage turbine. The turbine shaft is rotationally supported by a plurality of bearings all located on a same side of the compressor rotor(s) and all located on a same side of the turbine rotor(s), for example all located between the compressor rotor(s) and the turbine rotor(s), such that the compressor rotor(s) and the turbine rotor(s) are cantilevered. A method of driving a rotatable load of an aircraft is also discussed.