I need to be able to control the order of posts across different categories.

I have a client:
https://primarycare.hms.harvard.edu/

They have 4 category posts. When they write a post, they click on a category and that post gets uploaded into that post’s respective category page.

They now want to be able to write a post, and have it appear across multiple categories AND be able to control the order in which that post shows up within the post list.

Does anyone know of a plugin or solution for such a task?

Thanks