Multiple fault identification in induction motors is essential in industrial processes due to the high costs that unexpected failures can cause. In real cases, the motor could present multiple faults, influencing systems that classify isolated failures. This paper presents a novel methodology for detecting multiple motor faults based on quaternion signal analysis (QSA). This method couples the measured signals from the motor current and the triaxial accelerometer mounted on the induction motor chassis to the quaternion coefficients. The QSA calculates the quaternion rotation and applies statistics such as mean, variance, kurtosis, skewness, standard deviation, root mean square, and shape factor to obtain their features. After that, four classification algorithms are applied to predict motor states. The results of the QSA method are validated for ten classes: four single classes (healthy condition, unbalanced pulley, bearing fault, and half-broken bar) and six combined classes. The proposed method achieves high accuracy and performance compared to similar works in the state of the art.