It is important to study MULTIBODY dynamics when analyzing the transfer of cargo between ships and platforms at sea. The hydrodynamic interactions between multiple bodies in close proximity are expected to be significant and complex. In this paper, two levels of approximation of hydrodynamic coefficients are considered, i.e., the constant coefficient method (CCM) and the impulse response function (IRF). The equations of motion are written in standard state-space format, in which the convolution terms are computed using the trapezoidal rule. Initially, this newly proposed numerical scheme is successfully applied to calculate motion responses of a two-body floating system. The time-domain responses of this multibody floating system in both regular waves and random sea are further verified numerically. In addition, an ideal case of the motion mitigation of this system using Dynamic Positioning (DP) system is also given and discussed. The mean drift force is considered using Newmans approximation. Numerical study shows that the optimal Linear Quadratic Regulator (LQR) method can help to mitigate the motion responses of this two-body floating system at sea. Finally, this scheme is extended to a three-body floating system, with the relative motions in random seas determined.