Thank you for posting your query on Microsoft Q&A, from above description I could understand that you are looking for time bound recurring PIM assignment for global reader role.
Please do correct me if this is not the ask by responding in the comments section.
As of now we have only permanent or time bound assignment, but recurring assignment is not available in current design.
However, if this feature is impacting your business needs, I would recommend posting your feedback with business justification on our feedback portal as this is managed by our dev team.
If you don't have any further queries and the suggestion above answers your ask, please "Accept the answer", This will help us and others in the community as well.
Thanks,
Akshay Kaushik