A first host device establishes connectivity to a logical storage device of a storage system. The first host device obtains from the storage system host connectivity information identifying at least a second host device that has also established connectivity to the logical storage device, caches one or more extents of the logical storage device in a memory of the first host device, and maintains local cache metadata in the first host device regarding the one or more extents of the logical storage device cached in the memory of the first host device. In conjunction with processing of a write operation of the first host device involving at least one of the one or more cached extents of the logical storage device, the first host device invalidates corresponding entries in the local cache metadata of the first host device and in local cache metadata maintained in the second host device.