Multi-section semiconductor optical amplifiers (SOA) have been shown to have superior noise and linearity performance compared with single section SOAs. We show how to create a simplified numerical model for multi-section SOAs that is suitable for optical communication system simulations and use that model to investigate the amplification performance of 56 Gbit/s four-level pulse amplitude modulation signals. We find that a multi-section SOA could provide an improvement in input power dynamic range exceeding 3 dB compared to a single section SOA that has the same unsaturated gain.