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In-network computing provides significant performance benefits, load reduction, and power savings. Still, an in-network service's functionality is strictly limited to a single hardware device. Research has focused on enabling on-device functionality, with limited consideration to distributed in-network computing. This paper explores the applicability of distributed computing to in-network computing. We present DINC, a framework enabling distributed in-network computing, generating deployment strategies, overcoming resource constraints and providing functionality guarantees across a network. It uses multi-objective optimization to provide a deployment strategy, slicing P4 programs accordingly. DINC was evaluated using seven different workloads on both data center and wide-area network topologies, demonstrating feasibility and scalability, providing efficient distribution plans within seconds.