Within Teamwork Projects, you can quickly review and edit the access and permissions that a particular person has for multiple projects in the 'Project Access' screen.
Go to the 'People' section at the top of your screen:
From there, click the edit pencil that appears to the right when you hover over the person's name. Alternatively, click the person's name to open their profile, and then click the Edit button in the top right corner or their profile.
In the edit details modal, go to the 'Permissions' tab, and click the 'Edit' link next to the 'Project Access' total count at the bottom:
You will see a list of projects (grouped by the company they are associated to) with a preview of the permissions they have on that project.
You can use the padlock icon to quickly add this person to each project (or remove them), or multiple projects at once:
Note: If a user has the permission for 'Manage people and companies' enabled but is not a project admin on a particular project they will see the project in the list but will be unable to add a user to it.
This project will display a lock icon and the edit option will be removed:
Note: Any changes you make to access or permissions will be applied immediately so you can just click the 'Finished' button to exit this screen.
For more information see: Adding people to a project