Two PhD's in different UK universities, simultaneously, part-time: absurd idea? I have what might seem like the nicest problem in the world: I've got offered funding for both of my dream PhD's. I am stunned, incredulous, gobsmacked, but also deeply confused: both are with supervisors I would absolutely love to work with, both are topics that genuinely fascinate me. Having to choose one feels like Sophie's choice to me - as soon as I imagine choosing one I start grieving the other.
My question is, would it be madness to switch to part-time mode and pursue both? One is funded by ESRC and the other one, by AHRC; there are parallels in the subject matter but the projects and research methods are completely different, so there is no way I could unite the two (although my two prospective supervisors know and extensively quote each other). The field is humanities (cultural/visual studies in one case, same but with a good dash of social sciences in the other). 
Thank you!
Andrew mostly covered why this is administratively impossible, but I think it's also worth addressing the misunderstanding of what a Ph.D. is embedded in this question.  Pete Clark said it better than I can, but Ph.D.'s are not merit badges.  More is not better.  Getting a Ph.D. on one of these topics will not stop you from working on the other.  Working with one of these advisors officially will not stop you from staying in touch with the other, and potentially collaborating in the future.  You want to have ideas about other stuff to work on once you finish your dissertation.

I don't envy having to make the choice, and you will have to close one the doors part of the way to actually finish your degree.  But you don't have to slam it all the way shut, and you never know when ideas you know thought you had set to the side will come right back to you.