An approach to the concurrent design of the multiaxial inertial dampers for damping augmentation of the Multi-Body Dynamic (MBD) system is presented. The system considered herein features a 3-cable mechanism that acts as a suspension system equipped with the 3-axial inertial dampers atop a stable platform. Such a damping device has been introduced as an application in eliminating the attendant vibrations of the 3-cable suspension system for use in the preflight validation testing of flexible space structures. The primary objective is aimed at optimally designing three independent dampers in a concurrent procedure, in which an optimization is developed to minimize mean-squared motion in an attempt to augment damping of the 3-cable suspension system against the pendulum vibrations. This leads to the simultaneous tuning of three inertial dampers without any loss of cross-coupled damping effect from the MBD standpoint. Comparison of the simulated-time histories for the cases of damped and undamped vibrations is presented to show the effectiveness of the present approach.