If you are an Enterprise Administrator or have Team Leader access in a Project, you will be able to edit it's system Project Base Map. This setting will be saved in the database and shared across all Users. Here is how you would do this:
Search for Projects (1) and open up the Project Record (2) you would like to add a Project Base Map to.
Once the Project is opened (13), flick over to the Mapping tab (14), make your selections (15) and save the record (16)
That's it! It's all done. These changes made on the Project Record will be saved in the system database. This becomes the default Project Base Map when Users try to load map settings from the database and when they add a Project Map in the Mapping Tool.