Hello Juan 

Actually the +stage only appears for the group Project / Administrator

You can change this by customization
as you can see  in the following js code

async onWillStart() {
    if (this.props.list.isGroupedByStage) { // no need to check it if not grouped by stage
        this.isProjectManager = await this.userService.hasGroup('project.group_project_manager');
    }
}

in the line this.isProjectManager = await this.userService.hasGroup('project.group_project_manager');

odoo checks for the group Project / Administrator by id

So you can customize this code to search for Project / User

Another approach(which i don't recommend because it might give some unseen privileges) 

1. Duplicate the Project / Administrator Group and name it Project / Administrator Privileges
   
2. Remove all Access Rights from the Original Project / Administrator group
3. Assign the original Project / Administrator group to the users you want to create the stages
4. Assign the Project / Administrator Privileges group to the Project Administrators