The increasingly diversified Quality-of-Service (QoS) requirements envisioned for future wireless networks call for more flexible and inclusive multiple access techniques for supporting emerging applications and communication scenarios. To achieve this, we propose a multi-dimensional multiple access (MDMA) protocol to meet individual User Equipment's (UE's) unique QoS demands while utilizing multi-dimensional radio resources cost-effectively. In detail, the proposed scheme consists of two new aspects, i.e., selection of a tailored multiple access mode for each UE while considering the UE-specific radio resource utilization cost; and multi-dimensional radio resource allocation among coexisting UEs under dynamic network conditions. To reduce the UE-specific resource utilization cost, the base station (BS) organizes UEs with disparate multi-domain resource constraints as UE coalition by considering each UE's specific resource availability, perceived quality, and utilization capability. Each UE within a coalition could utilize its preferred radio resources, which leads to low utilization cost while avoiding resource-sharing conflicts with remaining UEs. Furthermore, to meet UE-specific QoS requirements and varying resource conditions at the UE side, the multi-dimensional radio resource allocation among coexisting UEs is formulated as an optimization problem to maximize the summation of cost-aware utility functions of all UEs. A solution to solve this NP-hard problem with low complexity is developed using the successive convex approximation and the Lagrange dual decomposition methods. The effectiveness of our proposed scheme is validated by numerical simulation and performance comparison with state-of-the-art schemes. In particular, the simulation results demonstrate that our proposed scheme outperforms these benchmark schemes by large margins.