Hi Lauren, this is possible, but completely unsupported by Tableau, please take a backup and do this at your own risk.
You need to access the Postgres DB using the superuser 'tblwgadmin' from the Tableau Server machine. See this link to find the password:
After that it's a matter of connecting to the PostgresDB using a SQL editor or psql command line, and adding a new user with whatever rights you choose. Here's a post I wrote on the subject a while back (scroll to the bottom). This was for v8 but it's broadly the same process.
What version of Server and...why?