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By introducing the bit-level multi-stream coded Layered Space-Time (LST) transmitter along with a novel iterative MultiStage Decoding (MSD) at the receiver, the paper shows how to achieve the near-capacity performance of the Multiple-Input Multiple-Output (MIMO) systems with square Quadrature Amplitude Modulation (QAM). In the proposed iterative MSD scheme, the detection at each stage is equivalent to multiuser detection of synchronous Code Division Multiple Access (CDMA) multiuser systems with the aid of the binary representation of the transmitted symbols. Therefore, the optimal Soft-Input Soft-Output (SISO) multiuser detection and low-complexity SISO multiuser detection can be utilized herein. And the proposed scheme with low-complexity SISO multiuser detection has polynomial complexity in the number of transmit antennas M, the number of receive antennas N, and the number of bits per constellation point Mc. Simulation results demonstrate that the proposed scheme has similar Bit Error Rate (BER) performance to that of the known Iterative Tree Search (ITS) detection.