We present Keigo, a concurrency- and workload-aware storage middleware that enhances the performance of log-structured merge key-value stores (LSM KVS) when they are deployed on a hierarchy of storage devices. The key observation behind Keigo is that there is no one-size-fits-all placement of data across the storage hierarchy that optimizes for all workloads. Hence, to leverage the benefits of combining different storage devices, Keigo places files across different devices based on their parallelism, I/O bandwidth, and capacity. We introduce three techniques - concurrency-aware data placement, persistent read-only caching, and context-based I/O differentiation. Keigo is portable across different LSMs, is adaptable to dynamic workloads, and does not require extensive profiling. Our system enables established production KVS such as RocksDB, LevelDB, and Speedb to benefit from heterogeneous storage setups. We evaluate Keigo using synthetic and realistic workloads, showing that it improves the throughput of production-grade LSMs up to 4x for write- and 18x for read-heavy workloads when compared to general-purpose storage systems and specialized LSM KVS.