Spatial multiplexing (SMX) multiple-input multiple-output (MIMO) over the best beamspace was considered as the best solution for millimeter wave (mm ave) communications regarding spectral efficiency (SE), referred as the best beamspace selection (BBS) solution. The equivalent MIMO water-filling (F-MIMO) channel capacity was treated as an unsurpassed SE upper bound. Recently, researchers have proposed various schemes trying to approach the benchmark and the performance bound. In this paper, we challenge the benchmark and the corresponding bound by proposing a better transmission scheme that achieves higher SE, namely the Generalized Beamspace Modulation using Multiplexing (GBMM). Inspired by the concept of spatial modulation, we not only use the selected beamspace to transmit information but also use the selection operation to carry information. e prove that GBMM is superior to BBS in terms of SE and can break through the well known upper bound. That is, GBMM renews the upper bound of the system SE. e investigate SE-oriented precoder activation probability optimization, fully-digital precoder design and hybrid precoder design for GBMM. Comparisons with the benchmark (i.e., F-MIMO channel capacity) are made under different system configurations to show the superiority of GBMM.