In this paper, we propose the berth allocation problem (BAP) with multiple ships being berthed at a specific berth, in order to enhance the efficient usage of the multi-user terminal system (MUT), which is planned to be introduced in major container ports in Japan for enormous port-related cost savings. The proposed berth allocation is expected to contribute in raising the efficiency of the MUT much more than the BAP with a single ship berthed at a berth, which was developed in an existing study. It was demonstrated that throughout a series of simulations for sophisticated container handling tasks in a terminal based on both BAP schemes, the BAP with multi-ships outperforms the one with a single ship in shortening the total waiting time as well as the total service time being spent while ships in port.