In this paper, we study the advantages of multi-user concurrent transmission, measured using the multi-user gain (MUG), in multiple-input multiple-output (MIMO) systems with rate constraints. Our focus is on a maximum eigenmode beamforming (MEB) strategy. We derive a closed-form expression for the transmitted sum power required by the MEB strategy and prove that this strategy is asymptotically optimal. The simple closed-form expression for the MEB sum-power provides many useful insights into the asymptotic behavior of multi-user MIMO systems. Interleave-division multiple-access is adopted as a platform for implementing the proposed MEB scheme. Both numerical and simulation results show that a major part of MUG can be achieved with a quite small number of users.