Enrollment Flows support multiple duplicate modes. In the case of an Invitation Enrollment Flow, if the duplicate mode is set to "Create new Role" or "Create new Role if Different COU," then the petition will fail with an error on subsequent executions of the flow, if a duplicate enrollment is detected.
To reproduce the issue:

• Create an invitation enrollment flow. Check the screenshot for the configuration options
• Invite a person to the COU X.
• Then invite the same person to the COU Y.

Both Enrollment Flow Forms have the same person info, given name, family name, email, role title. The only difference is the COU choice.

Duplicate detection works as expected. Check the screenshot below.