Method embodiments for facilitating overflow storage of special data sets that reside on a single logical volume are provided. A virtual logical volume is created from unallocated memory units across a plurality of logical volumes in a volume group. The virtual logical volume appears the same as any one of the logical volumes in the volume group to an external client. Upon receipt of a special data set that must reside in a single logical volume, an attempt is first made to allocate the special data set to one of the logical volumes in the volume group. If that allocation attempt fails, the special data set is allocated to the virtual logical volume. The virtual logical volume may be created only upon the failure to allocate the special data set to one of the logical volumes, and may be destroyed if sufficient space in one of the logical volumes is freed up to transfer the special data set. Creation of the virtual logical volume may be reserved for only critical special data sets whose failure would result in a storage system outage.