Hyper-V provides one setting that you can configure for storage migration.  The maximum number of storage migrations you can have happening at the same time:

image

By default this is set to “2”.  If you try to perform more than this – you will receive an error message that tells you that you are at your limit.  If you want to change this setting (I usually set it to 10) the only thing you need to consider is if your physical storage is up to having that much I/O occurring at one point in time.  My systems tend to have SSD disks or to be configured in RAID 10 and are able to handle a larger number of simultaneous storage migrations comfortably.

Cheers,
Ben