Rate splitting (RS) has emerged as a valuable technology for wireless communications systems due to its capability to deal with uncertainties in the channel state information at the transmitter (CSIT). RS with linear and non-linear precoders, such as the Tomlinson-Harashima (THP) precoder, have been explored in the downlink (DL) of multiuser multi antenna systems. In this work, we propose a multi-branch (MB) scheme for a RS-based multiple-antenna system, which creates patterns to order the transmitted symbols and enhances the overall sum rate performance compared to existing approaches. Closed-form expressions are derived for the sum rate through statistical analysis. Simulation results show that the proposed MB-THP for RS outperforms conventional THP and MB-THP schemes.