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Data-intensive augmented information (AgI) services (e.g., metaverse applications such as virtual/augmented reality), designed to deliver highly interactive experiences resulting from the real-time combination of live data-streams and pre-stored digital content, are accelerating the need for distributed compute platforms with unprecedented storage, computation, and communication requirements. To this end, the integrated evolution of next-generation networks (5G/6G) and distributed cloud technologies (mobile/edge/cloud computing) have emerged as a promising paradigm to address the interaction- and resource-intensive nature of data-intensive AgI services. In this paper, we focus on the design of control policies for the joint orchestration of compute, caching, and communication (3C) resources in next-generation 3C networks for the delivery of data-intensive AgI services. We design the first throughput-optimal control policy that coordinates joint decisions around (i) routing paths and processing locations for live data streams, with (ii) cache selection and distribution paths for associated data objects. We then extend the proposed solution to include a max-throughput data placement policy and two efficient replacement policies. Numerical results demonstrate the superior performance obtained via the novel multi-pipeline flow control and 3C resource orchestration mechanisms of the proposed policy, compared with state-of-the-art algorithms that lack full 3C integrated control.