Multi-motor drive systems (MMDS) combine several drives that work together to fulfill one task. Compared to conventional single-motor drive systems modular product concepts can be realized with MMDS thanks to additional degrees of freedom. Because of their mechanical structure consisting of several shafts, clutches, and gear pairings, complex deflection shapes arise which lead to unintended torque oscillations.To compensate for these torque oscillations a data-driven adaptive multiple-input single-output scheme based on two cascaded recursive least squares estimators is proposed. Here, weights (manipulable amplitudes) for each order (multiple of a fundamental frequency) to be compensated are multiplied with unit amplitude harmonic signals of a reference oscillator and added as reference torques to the torque controllers of the MMDS's drives. These weights are continually adapted by an online identification of transfer paths and disturbances. Furthermore, the torque contribution of the individual drives concerning the compensation task can be changed at runtime utilizing a weighting matrix as tuning parameter by analytically solving a quadratic program with a linear equality constraint. Hence, the proposed algorithm is suitable for automatic self-commissioning requiring only marginal expert intervention. Experimental investigations prove the compensation capability of the approach whereby a reduction of the output torque's total harmonic distortion (THD) of up to 80% from 26.8% to 5.4% for a representative operation point is achieved.