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Reconfigurable intelligent surface (RIS)-assisted communications appear as a promising candidate for future wireless systems due to its attractive advantages in terms of implementation cost and end-to-end system performance. In this paper, two new multiple-input multiple-output (MIMO) system designs using RISs are presented to enhance the performance and boost the spectral efficiency of state-of-the-art MIMO communication systems. Vertical Bell Labs layered space-time (VBLAST) and Alamouti's schemes have been considered in this study and RIS-based simple transceiver architectures are proposed. For the VBLAST-based new system, an RIS is used to enhance the performance of the nulling and canceling-based sub-optimal detection procedure as well as to noticeably boost the spectral efficiency by conveying extra bits through the adjustment of the phases of the RIS elements. In addition, RIS elements have been utilized in order to redesign Alamouti's scheme with a single radio frequency (RF) signal generator at the transmitter side and to enhance its bit error rate (BER) performance. Monte Carlo simulations are provided to show the effectiveness of our system designs and it has been shown that they outperform the reference schemes in terms of BER performance and spectral efficiency.