As the foundation of the Web3 trust system, blockchain technology faces increasing demands for scalability. Sharding emerges as a promising solution, but it struggles to handle highly concurrent cross-shard transactions (\textsf{CSTx}s), primarily due to simultaneous ledger operations on the same account. Hyperledger Fabric, a permissioned blockchain, employs multi-version concurrency control for parallel processing. Existing solutions use channels and intermediaries to achieve cross-sharding in Hyperledger Fabric. However, the conflict problem caused by highly concurrent \textsf{CSTx}s has not been adequately resolved. To fill this gap, we propose HiCoCS, a high concurrency cross-shard scheme for permissioned blockchains. HiCoCS creates a unique virtual sub-broker for each \textsf{CSTx} by introducing a composite key structure, enabling conflict-free concurrent transaction processing while reducing resource overhead. The challenge lies in managing large numbers of composite keys and mitigating intermediary privacy risks. HiCoCS utilizes virtual sub-brokers to receive and process \textsf{CSTx}s concurrently while maintaining a transaction pool. Batch processing is employed to merge multiple \textsf{CSTx}s in the pool, improving efficiency. We explore composite key reuse to reduce the number of virtual sub-brokers and lower system overhead. Privacy preservation is enhanced using homomorphic encryption. Evaluations show that HiCoCS improves cross-shard transaction throughput by 3.5-20.2 times compared to the baselines.