In this work, we unveil the advantages of synergizing cooperative rate splitting (CRS) with user relaying and simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR RIS). Specifically, we propose a novel STAR RIS-assisted CRS transmission framework, featuring six unique transmission modes that leverage various combination of the relaying protocols (including full duplex-FD and half duplex-HD) and the STAR RIS configuration protocols (including energy splitting-ES, mode switching-MS, and time splitting-TS). With the objective of maximizing the minimum user rate, we then propose a unified successive convex approximation (SCA)-based alternative optimization (AO) algorithm to jointly optimize the transmit active beamforming, common rate allocation, STAR RIS passive beamforming, as well as time allocation (for HD or TS protocols) subject to the transmit power constraint at the base station (BS) and the law of energy conservation at the STAR RIS. To alleviate the computational burden, we further propose a low-complexity algorithm that incorporates a closed-form passive beamforming design. Numerical results show that our proposed framework significantly enhances user fairness compared with conventional CRS schemes without STAR RIS or other STAR RIS empowered multiple access schemes. Moreover, the proposed low-complexity algorithm dramatically reduces the computational complexity while achieving very close performance to the AO method.