By investigating the conditions required for successive interference cancellation multiuser detectors (SIC-MUD) to achieve near-optimum BER performance, we propose and investigate a so-called receiver multiuser diversity aided multi-stage minimum mean-square error MUD (RMD/MS-MMSE MUD), which is operated in the SIC principles. The BER performance of the RMD/MS-MMSE MUD is investigated in association with both the direct-sequence code-division multiple-access (DS-CDMA) over either Gaussian or Rayleigh fading channels, and the space-division multiple-access (SDMA) over Rayleigh fading channels. Furthermore, we consider both full-load and overload scenarios in comparison with the spreading factor N of DS-CDMA and the number of receive antennas N in SDMA. Our studies show that the RMD/MS-MMSE MUD is highly efficient for both full-load and overload systems. Specifically, the RMD/MS-MMSE MUD for the full-load systems of moderate size is capable of attaining the BER performance similar to that of the optimum maximum likelihood MUD (ML-MUD). For the overload systems, it can allow a DS-CDMA or SDMA system to support K=2N users and still achieve much better BER performance than a corresponding DS-CDMA or SDMA system using conventional MMSE-MUD to support K=N users.