In the context of a social sciences PhD in the UK, I want to know (i) whether it is permissible to work on another research project; and (ii) whether there are any general practices, if I choose to work on a research project with a professor in a different university, in addition to my existing PhD research project with my main supervisor. The topics of my main PhD research project and the other project are closely linked.
Not sure if this is relevant, but both my main supervisor and the other professor at a different university frequently collaborate on projects.
Edit: I asked my advisor about this, and she stated it was fine (and we had to figure out details), but I could sense that she was very hesitant about it. I am not sure if I offended her by asking at all, but I am very keen to work on this other project.