1. A method of managing data storage operations, comprising: directing a data storage array coupled to a storage processor to provision a set of storage resources on the array for storing multiple file systems of a VSP (virtualized storage processor) operated by the storage processor; operating multiple VSPs, including the VSP, on the storage processor, each of the VSPs including a respective plurality of file systems stored in a respective set of storage resources on the array such that each set of storage resources on the array is exclusive to a respective one of the VSPs; in response to the storage processor receiving file-based requests to access files of the file systems of the VSP, sending block-based requests to the array to access content of the files from the set of storage resources; and in response to an issuance of a management command to perform a data operation on the VSP, directing the array to perform the data operation on each of the set of storage resources for the VSP but not on any sets of storage resources of other VSPs of the multiple VSPs, thereby effecting the data operation by the array exclusively on the file systems of the VSP together as a group.