Methods and systems for an electric drive axle of a vehicle are provided. A gear train in an electric drive axle system includes, in one example, an input shaft configured to rotationally couple to an electric motor-generator and including a first gear and an intermediate shaft including a second gear rotationally coupled to the first gear and a third gear and a fourth gear each configured to rotationally couple to a separate gear on an output shaft. In this example, the second gear, the third gear, and the fourth gear have different sizes, the third gear includes an axial extension having at outer surface, and an interior surface of the second gear circumferentially surrounds at least a portion of the outer surface of the axial extension.