Due to the growing complexity of vertical applications, current integrated sensing and communications (ISAC) in wireless networks remains insufficient for supporting all required beyond communication services. To this end, future networks are evolving toward an integrated heterogeneous service provisioning (IHSP) platform, which seeks to integrate a broad range of heterogeneous services beyond the dual-function scope of ISAC. Nevertheless, this trend intensifies conflicts among concurrent heterogeneous service requirements under constrained resource sharing. In this paper, we overcome this challenge by the joint use of two novel elastic design strategies: compromised service value assessment and flexible multi-dimensional resource multiplexing. Consequently, we propose a value-prioritized elastic multi-dimensional multiple access (MDMA) mechanism for IHSP systems. First, we modify the Value-of-Service (VoS) metric by incorporating elastic parameters to characterize user-specific tolerance and compromise in response to various performance degradations under constrained resources. This VoS metric serves as the foundation for prioritizing services and enabling effective fairness service scheduling among concurrent competing demands. Next, we adapt the MDMA to elastically multiplex services using appropriate multiple access schemes across different resource domains. This protocol leverages user-specific interference tolerances and cancellation capabilities across different domains to reduce resource-demanding conflicts and co-channel interference within the same domain. Then, we maximize the system's VoS by jointly optimizing MDMA and power allocation. Since this problem is non-convex, we develop a monotonic optimization-assisted dynamic programming algorithm for the optimal solution and a VoS-prioritized successive convex approximation algorithm for efficient suboptimal computation.
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