In this paper, multi-electron interactions for low-charge-state ions in heavy ion beam fusions (HIBF) is studied through exploring theoretical approaches and developing improved models. An improved classic trajectory Monte Carlo model and corresponding codes have been built to implement those simulations, mainly though the intensive computations in solving many-body Hamiltonian Equations. Following the results present in the previous meetings (Ref. 1-2), the results here for the low-charge-state ions of Xe, Bi and other ions colliding with noble gas are provided, and show that multi-electron effects are obvious and their cross section can reach about 40% of the total cross section. The improved code employs parallel computing, and is expected to be an integral part of a plasma simulation package to study the atomic effects in plasma beam transportation and focusing in HIBF, and help to provide improved physical insight into current HIBF experiments and future studies.