In one aspect the present subject matter is directed to a system for supporting shafts of an indirect-drive turbofan engine. The system includes a fan frame assembly that is coaxially aligned with a centerline of the turbofan engine and positioned forward of a reduction gear that couples a low pressure rotor shaft to a fan shaft. A compressor frame assembly is aligned with the centerline aft of the reduction gear and is positioned axially between a low pressure compressor and a high pressure compressor of the turbofan engine. A turbine frame assembly is coaxially aligned with the centerline and is positioned axially between a high pressure turbine and a low pressure turbine of the turbofan engine. The turbine frame assembly rotatably supports an aft end portion of a high pressure rotor shaft and an aft end portion of the low pressure rotor shaft.