For a multi-way relay network (MWRN) with K users, K time slots are needed for full data exchange. Thus, the overall spectral efficiency, due to the 1/K pre-log factor, declines as number of users grows. It has recently been improved to roughly K/2 time slots, but even this improvement does not arrest the decline. Herein, we reduce this task to just two time slots regardless of K. To do this, we exploit the performance gains of non-orthogonal multiple-access (NOMA) and a massive multiple-input multiple-output (MIMO) relay. First, the users transmit their signals to the relay, which uses maximal ratio combining reception. Next, the relay transmits a superposition-coded signal for all users by using maximal ratio transmission. Each user then performs successive interference cancellation (SIC) decoding of data symbols of the other K - 1 user nodes. We use the so-called worst-case Gaussian approximation to derive the overall sum rate and demonstrate significant spectral-efficiency gains and energy-efficiency gains over the existing MWRN counterparts. We also design the relay power allocation matrix to maximize the minimum among the user rates, thus maximizing the user fairness. Furthermore, the effects of imperfect SIC and imperfect channel state information (CSI) on the sum rate are analyzed.