1. A data storage subsystem for providing cross data storage device communication for a move operation, the data storage subsystem comprising: a first data storage device including a first non-volatile memory; and a second data storage device including a second non-volatile memory; wherein the first data storage device is to: transmit, in response to a move request that identifies a block of data to be moved from the first data storage device to the second data storage device, a completion notification to a processor; read, after transmitting the completion notification, the block of data from the first non-volatile memory to a volatile memory; and transmit, to the second data storage device, a second move request to move the block of data; and the second data storage device is to: write, in response to the second move request, the block of data from the volatile memory to the second non-volatile memory of the second data storage device.