As a Process Owner, you have the following permissions for inviting new members :
Process-specific: You can invite other users to join your assigned Process. For Example if you are the Process Owner for Proc1, you can invite another Process Owners to control the same.
Hierarchical Control: You can assign new members as Process Owners within your assigned Process.
Limitations: You cannot invite users to processes that you do not own. For example if you are the Process Owner for Proc1, you cannot invite user to other processes such as Proc2 and Proc3 mapped to your account.