We consider a multi-way relay network with multiple users exchanging information with each other via a multi-antenna relay. The multi-way relaying strategy consists of one multiple access phase and multiple broadcast phases. We jointly design relay beamforming matrices and users’ linear processing receivers in the broadcast phases to maximize the minimum signal-to-interference-and-noise ratio (SINR) under the relay power budget. For the non-convex joint optimization problem, we propose to solve it by iteratively optimizing the relay beam matrices and receiver processing matrices in two sub-problems. For the receiver processing, both maximum-ratio-combining (MRC) receiver and zero-forcing (ZF) receiver are designed. We show that our iterative approach with the MRC receiver leads to a local maximum for the original joint optimization problem, while the ZF receiver has the computational advantage with a lower complexity. To further improve the performance, we design the successive interference cancellation at each user’s receiver based on the SINR criterion to sequentially decode symbols from other users. Simulation shows that our proposed algorithm for joint design provides substantial improvement in the sum rate than the existing methods that use the sum rate as the design objective. Finally, we investigate the performance of our proposed algorithm under partial channel state informations (CSIs). We show in simulation that using quantized CSIs at each receiver only incurs a small performance loss for the typical range of relay channel quality.