An integrated device is provided that includes a non-volatile memory having an addressing parallelism and a data parallelism, and a communication interface for interfacing the memory with an external bus. The external bus has a transfer parallelism lower than the addressing parallelism and the data parallelism. The communication interface includes control means for executing multiple reading operations and/or multiple writing operations on the memory according to different modalities in response to corresponding command codes received from the external bus. Also provided is a method of operating such an integrated device.