Multiple people can analyze one project as long as they have the proper privileges to read/edit it.  A Published project must first be downloaded to a users “Server Projects” folder or “Local machine” folder before it can edited. Once edited, it can publish back to the Master server, either overwriting the existing project (it they have the privileges) or as new project.

All projects must have a unique name, so Array Studio will warn the user if they are trying to save a project that already exists on the server (they must have “edit” access to that project):

The user has the option to use a unique name if they don’t want to overwrite the original server project. If they don’t have “edit” access, they are forced to supply a unique name for the project being published.