Public blockchains inherently offer low throughput and high latency, motivating off-chain scalability solutions such as Payment Channel Networks (PCNs). However, existing PCNs suffer from liquidity fragmentation-funds locked in one channel cannot be reused elsewhere-and channel depletion, both of which limit routing efficiency and reduce transaction success rates. Multi-party channel (MPC) constructions mitigate these issues, but they typically rely on leaders or coordinators, creating single points of failure and providing only limited flexibility for inter-channel payments. We introduce Hypergraph-based Multi-Party Payment Channels (H-MPCs), a new off-chain construction that replaces bilateral channels with collectively funded hyperedges. These hyperedges enable fully concurrent, leaderless intra- and inter-hyperedge payments through verifiable, proposer-ordered DAG updates, offering significantly greater flexibility and concurrency than prior designs. Our implementation on a 150-node network demonstrates a transaction success rate of approximately 94% without HTLC expiry or routing failures, highlighting the robustness of H-MPCs.