Can I have two PhD supervisors from two different UK universities? I have two unconditional offers from two UK universities in law. University A assigned me one supervisor only, but he is the greatest in part of my thesis. University B also assigned me one supervisor, who also has a very unique insight in the second part of my thesis.
Is there any possibility to ask for a joint PhD? Or any way to be collaboratively supervised by these two great supervisors? If any one has a successful similar situation, I will be grateful if you could share it.
As the old saying goes, if you don't ask, you don't get. In my experience it's quite common to have an external supervisor on the team, either from another university or from an industrial partner. So you can certainly ask.
How you approach the topic may depend on how well you already know the potential supervisors. If you have already built up a relationship with one of them, you can easily broach the question in an email. Chances are that the two potential supervisors will already know each other, if they work in a similar field. (Of course there's a chance this could work to your disadvantage, if they know each other and don't get on.)
If you don't already have a rapport with one or other of them, I would ask for a video call to discuss the offer they have made you. Prepare a few different, relevant questions, both about the research ideas and the logistical aspects of the position. Then you can bring up the other supervisor, while clearly emphasising that ideally you would like to be split 50/50 between them, and benefit from both their inputs.
If they agree, great! Your university likely has some official mechanism to add external people to your supervisory team. If they don't agree, that's not so good for you, but you could still consider collaborating informally with one of them later on.
Finally, remember that research is very changeable, and what you think your thesis will be about now might be very different from what you actually end up finding and writing about. So don't worry too much if you find yourself going in direction C, D or E rather than A and B.