Spatial multiplexing (SMX) multiple-input multiple-output (MIMO) over the best beamspace was considered as the best solution for millimeter wave (mmWave) communications regarding spectral efficiency (SE), referred as the best beamspace selection (BBS) solution. The equivalent MIMO water-filling (WF-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. But, are they the real limit of mmWave MIMO systems with reduced radio-frequency (RF) chains? 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, besides the selected beamspace, the selection operation is used to carry information. We 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 SE. We investigate SE-oriented precoder activation probability optimization, fully-digital precoder design, optimal power allocation and hybrid precoder design for GBMM. A gradient ascent algorithm is developed to find the optimal solution, which is applicable in all signal-to-noise-ratio (SNR) regimes. The best solution is derived in the high SNR regime. Additionally, we investigate the hybrid receiver design and deduce the minimum number of receive RF chains configured to gain from GBMM in achievable SE. We propose a coding approach to realize the optimized precoder activation. An extension to mmWave broadband communications is also discussed. Comparisons with the benchmark (i.e., WF-MIMO channel capacity) are made under different system configurations to show the superiority of GBMM.