you have to create a privilege set and grant it the privilege you want (view only, add certain date, modify certain table, view only project that user creation = ...),
and the set your users to that privilege set.
That is the insight I needed. So if I want to be able to add people to a project I would probably add a Table or field with for names and the the privilage set would check if they created or are in the list of people assigned.
Is there a way to interact with the filemaker database account like a table, creating relationships?
For what you want:
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a detailed description of how to set this up.