In this work, we investigate multiple access schemes for orthogonal time frequency space (OTFS), orthogonal time sequency multiplexing modulation (OTSM), and block-based single-carrier (SC) systems. We also develop two iterative receivers for multi-user reception in the uplink for these waveforms, considering practical pulse shapes, based on the principles of successive interference cancellation (SIC) and turbo decoding, respectively. We show an improvement in coded performance in multi-user scenarios compared to single-user scenarios for all three waveforms using both receivers. This contrasts with earlier reported results of uncoded error performance for multi-user OTFS, where degradation is observed between single-user and multi-user scenarios. We finally compare these waveforms in the presence of nonlinear effects of high-power amplifiers (HPAs) and we observe that the block SC performs best and stands to challenge the OTFS and OTSM.