This paper presents the design and development of a robotic system to give physical assistance to the elderly or people with neurological disorders such as Ataxia or Parkinson's. In particular, we propose using a mobile collaborative robot with an interaction-assistive whole-body interface to help people unable to maintain balance. The robotic system consists of an Omni-directional mobile base, a high-payload robotic arm, and an admittance-type interface acting as a support handle while measuring human-sourced interaction forces. The postural balance of the human body is estimated through the projection of the body Center of Mass (CoM) to the support polygon (SP) representing the quasi-static Center of Pressure (CoP). In response to the interaction forces and the tracking of the human posture, the robot can create assistive forces to restore balance in case of its loss. Otherwise, during normal stance or walking, it will follow the user with minimum/no opposing forces through the generation of coupled arm and base movements. As the balance-restoring strategy, we propose two strategies and evaluate them in a laboratory setting on healthy human participants. Quantitative and qualitative results of a 12-subjects experiment are then illustrated and discussed, comparing the performances of the two strategies and the overall system.