Is there a limit for concurrently running online/offline migrations between PVC/PSBM/PCS servers?
Other than memory dump restoration (which has a global in-kernel lock), there is no limit to the number of simultaneously running online migrations via command line apart from server and network resources/capacity limitations.
If you perform the migration in Parallels Virtual Automation, its internal limits could be hit, not allowing another migration task to be processed. Examples: queue limit for a specific PVA operator, heavy pool limitation (migration is considered as a heavy task), etc.
Please check the following article for additional questions about online migration: PVC for Linux best practices.