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We propose a novel multi-user multiple-input multiple-output (MIMO) technique termed the layered multi-group steered space-time shift keying (LMG-SSTSK) for the downlink of millimeter wave (mmWave) communications, which combines the concepts of multi-user MIMO, space-time shift keying, beamforming and orthogonal frequency-division multiplexing to simultaneously convey information to multiple users. The LMG-SSTSK tackles the propagation challenges of the high-attenuation mmWave frequencies by sub-dividing the users into multiple groups. The proposed system allows more users to be served simultaneously in the downlink over the same time- and frequency-resources than a system dispensing with the proposed grouping technique.