Intelligent reflecting surface (IRS) is envisioned to become a key technology for the upcoming six-generation (6G) wireless system due to its potential of reaping high performance in a power-efficient and cost-efficient way. With its disruptive capability and hardware constraint, the integration of IRS imposes some fundamental particularities on the coordination of multi-user signal transmission. Consequently, the conventional orthogonal and non-orthogonal multiple-access schemes are hard to directly apply because of the joint optimization of active beamforming at the base station and passive reflection at the IRS.  Relying on an alternating optimization method, we develop novel schemes for efficient multiple access in IRS-aided multi-user multi-antenna systems in this paper. Achievable performance in terms of the sum spectral efficiency is theoretically analyzed. A comprehensive comparison of different schemes and configurations is conducted through Monte-Carlo simulations to clarify which scheme is favorable for this emerging 6G paradigm.