With the rapid development of offshore renewable energy technologies, open source solvers for hydrodynamic analysis can become beneficial to meet the numerical challenges within the field, particularly when they are both accurate and computationally efficient. Hydrodynamic Analysis of Marine Structures (HAMS), a recently developed open source Boundary Integral Equation Method (BIEM) frequency domain solver has been shown to be a reliable, robust and computationally efficient for analysing single floating structures. This research enhances the capabilities of HAMS further by developing and incorporating a multiple body interaction formulation (henceforth referred as HAMS-MREL), which allows the solution of the diffraction and the radiation problem for multiple floating structures, taking into account their interaction. To evaluate proper performance of this new multi-body solver, comparisons are performed with semi-analytical solutions, as well as with the commercial solver WAMIT in terms of the hydrodynamic coefficients and exciting forces. The excellent comparison with semi-analytical solutions demonstrates the validity of the enhanced multi-body version of HAMS. In addition, the computational comparison considering lower order panels between HAMS-MREL and WAMIT (no symmetry) show that for deep water cases, HAMS-MREL is generally faster than WAMIT, while for the finite depth cases, it is slower. Finally, the functionality to utilize OpenMP parallelization within the multi-body formulation has been added, aiming to reduce the analysis time significantly for the finite depth cases, offering an expected improvement for the future.