Supernumerary robotic arms (SRAs) can be used as the third arm to complement and augment the abilities of human users. The user carrying a SRA forms a connected kinodynamic chain, which can be viewed as a special class of floating-base robot systems. However, unlike general floating-base robot systems, human users are the bases of SRAs and they have their subjective behaviors/motions. This implies that human body motions can unintentionally affect the SRA's end-effector movements. To address this challenge, we propose a framework to compensate for the human whole-body motions that interfere with the SRA's end-effector trajectories. The SRA system in this study consists of a 6-degree-of-freedom lightweight arm and a wearable interface. The wearable interface allows users to adjust the installation position of the SRA to fit different body shapes. An inertial measurement unit (IMU)-based sensory interface can provide the body skeleton motion feedback of the human user in real time. By simplifying the floating-base kinematics model, we design an effective motion planner by reconstructing the Jacobian matrix of the SRA. Under the proposed framework, the performance of the reconstructed Jacobian method is assessed by comparing the results obtained with the classical nullspace-based method through two sets of experiments.