Spatial modulation (SM) transmits additional information bits by the selection of antennas. Generalized spatial modulation (GSM), as an advanced type of SM, can be divided into diversity and multiplexing (MUX) schemes according to the symbols carried on the selected antennas are identical or different. Recently, reconfigurable intelligent surface (RIS) assisted SM exhibits better reception performance compared to conventional SM. To overcome the limitations of SM, this paper combines GSM with RIS and proposes the RIS-aided receive generalized spatial modulation (RIS-RGSM) scheme. The RIS-RGSM diversity scheme is realized via a simple improvement based on the state-of-the-art scheme. To further increase the transmission rate, a novel RIS-RGSM MUX scheme is proposed, where the reflection phase shifts and on/off states of RIS elements are configured to achieve bit mapping. The theoretical bit error rate (BER) of the proposed scheme is derived and agrees well with the simulation results. Numerical simulations show that the RIS-RGSM MUX scheme has better BER performance than the diversity scheme. The proposed scheme can significantly increase the transmission rate and maintain good performance compared to the existing scheme under a limited number of antennas.