The upper 6 GHz band (U6 GHz, 6.425-7.125 GHz) has been identified as a new international mobile telecommunication (IMT) spectrum in the World Radiocommunication Conference 2023 (WRC-23). In the recent six generation (6G) workshop of the 3rd Generation Partnership Project (3GPP), the U6 GHz band is also anticipated as a potential 6G core spectrum. Additionally, the industry at the 6G workshop shares a common vision to obtain significant spectral efficiency gain for the user for not being at the expense of excess energy consumption or excess transmit power. To meet the 6G vision for the U6 GHz band, it is promising to apply the extreme receive antennas (ERA)-aided multi-input-multi-output (MIMO) with the receive antennas in the mobile device at least twice the spatial streams in the MIMO system. For example, by applying 12×4 or 8×4 MIMO (12 or 8 receive antennas in the mobile device for 4 spatial streams), user experienced spectral efficiency can reach up to 37 bps/Hz in this study, which is more than twice that of the current fifth generation (5G) 4×4 MIMO with the same 4 spatial streams. Note that the significant spectral efficiency gain is obtained with the same transmit power as compared to 4×4 MIMO at the base station. However, for the mobile device, to accommodate sufficiently many receive antennas for the ERA-aided MIMO application is a challenging task. For this application, we present an extremely low profile (ELP, 0.5 mm only) four-antenna module covering the U6 GHz band for MIMO communications. To our knowledge, the ELP four-antenna module has the smallest thickness (0.5 mm only) among related MIMO antenna modules reported to cover the U6 GHz band. The ELP feature allows the four-antenna module to be easily accommodated in the backcover region of modern mobile devices. By applying three ELP four-antenna modules, the mobile device can conveniently be equipped with 12 MIMO antennas. We present details of the ELP four-antenna module and fabricate three of them mounted in a smartphone-like device for 4×4 , 8×4 , and 12×4 MIMO performance evaluation. Note that the 12×4 MIMO has not yet been reported and is demonstrated for the first time in this study. The results obtained indicate that the ELP four-antenna module works for the ERA-aided MIMO with four spatial streams to achieve significant spectral efficiency gain in the U6 GHz band.