Large-scale MIMO systems can yield a substantial improvement in spectral efficiency for future communication systems. Due to the finer spatial resolution achieved by a huge number of antennas at the base stations, these systems have shown to be robust to inter-user interference and the use of linear precoding is asymptotically optimal. However, most precoding schemes exhibit high computational complexity as the system dimensions increase. For example, the near-optimal RZF requires the inversion of a large matrix. This motivated our companion paper, where we proposed to solve the issue in single-cell multi-user systems by approximating the matrix inverse by a truncated polynomial expansion (TPE), where the polynomial coefficients are optimized to maximize the system performance. We have shown that the proposed TPE precoding with a small number of coefficients reaches almost the performance of RZF but never exceeds it. In a realistic multi-cell scenario involving large-scale multi-user MIMO systems, the optimization of RZF precoding has thus far not been feasible. This is mainly attributed to the high complexity of the scenario and the non-linear impact of the necessary regularizing parameters. On the other hand, the scalar weights in TPE precoding give hope for possible throughput optimization. Following the same methodology as in the companion paper, we exploit random matrix theory to derive a deterministic expression for the asymptotic SINR for each user. We also provide an optimization algorithm to approximate the weights that maximize the network-wide weighted max-min fairness. The optimization weights can be used to mimic the user throughput distribution of RZF precoding. Using simulations, we compare the network throughput of the TPE precoding with that of the suboptimal RZF scheme and show that our scheme can achieve higher throughput using a TPE order of only 3.