The rapid evolution and convergence of wireless technologies and vertical applications have fundamentally reshaped our lifestyles and industries. Future wireless networks, especially 6G, are poised to support a wide range of applications enabled by heterogeneous services, leveraging both traditional connectivity-centric functions and emerging beyond-communication capabilities, particularly localization, sensing, and synchronization. However, integrating these new capabilities into a unified 6G paradigm presents significant challenges. This article provides an in-depth analysis of these technical challenges for integrative 6G design and proposes three strategies for concurrent heterogeneous service provisioning, with the aggregated goal of maximizing integration gains while minimizing service provisioning overhead. First, we adopt multi-dimensional multiple access (MDMA) as an inclusive enabling platform to flexibly integrate various capabilities by shared access to multidimensional radio resources. Next, we propose value-oriented heterogeneous service provisioning to maximize the integration gain through situation-aware MDMA. To enhance scalability, we optimize control and user planes by eliminating redundant control information and enabling service-oriented prioritization. Finally, we evaluate the proposed framework with a case study on integrated synchronization and communication, demonstrating its potential for concurrent heterogeneous service provisioning.