Millimeter wave (mmWave) communication has attracted increasing attention as a promising technology for 5G networks. One of the key architectural features of mmWave is the use of massive antenna arrays at both the transmitter and the receiver sides. Therefore, by employing directional beamforming (BF), both mmWave base stations (MBSs) and mmWave users (MUEs) are capable of supporting multi-beam simultaneous transmissions. However, most researches have only considered a single beam, which means that they do not make full potential of mmWave. In this context, in order to improve the performance of short-range indoor mmWave networks with multiple reflections, we investigate the challenges and potential solutions of downlink multi-user multi-beam transmission, which can be described as a high-dimensional (i.e., beamspace) multi-user multiple-input multiple-output (MU-MIMO) technique, including multi-user BF training, simultaneous users grouping, and multi-user multibeam power allocation. Furthermore, we present the theoretical and numerical results to demonstrate that beamspace MU-MIMO compared with single beam transmission can largely improve the rate performance of mmWave systems.