User permissions for specific site


I have a multisite network setup. The main site has a custom post type called "Ideas". I need to allow any logged in user from the whole network to be able to submit a front end form to create an Idea post. I have this working correctly using the ACF plugin to create the front end form.

The problem I have is it appears that anyone registered below the Editor user level doesn't have the required permissions to add post tags when submitting the form. They can only choose from existing tags, presumably because they don't have the manage_categories capability or something.

So my question is can anyone think of a way to grant all user roles the capabilities to add post tags just for this post type on this site? Or am I thinking about it the wrong way...?

Thanks for any suggestions!