1. A method for handling multi-volume datasets within a tape storage system, said method comprising: building a chain of logical volume names that belongs to a multi-volume dataset by utilizing a plurality of clone LUM volume mount commands, wherein each of said plurality of clone LUM volume mount commands is captured in response to an access request for a virtual volume by a host computer, wherein said virtual volume belongs to said multi-volume dataset generated by an application within said host computer having an Advanced Policy Management enabled such that a Library Universal Mount (LUM) for each subsequent mount for said access request contains a name of a first or previous virtual volume in said multi-volume dataset as a “clone” source virtual volume; storing said chain of logical volume names in a chain database within an automatic storage management administrator of said tape storage system; in response to an access request for a virtual volume N within said multi-volume dataset, determining whether or not the percentage of time for all virtual volumes in said multi-volume dataset to be accessed when said virtual volume N was previously requested is greater than a first high threshold; and in a determination that the percentage of time for all virtual volumes in said multi-volume dataset to be accessed when said virtual volume N was previously requested is greater than said first high threshold, recalling all virtual volumes in said multi-volume dataset.