What if we were all connected in some way? Across time? Across space?

As the last of his kind, the Doctor feels doomed to be alone until he meets a pushy medical student who worms her way first into his bed and then his heart. Suddenly he realised he doesn't have to be alone, but can he make himself take that last, unthinkable step? Starting with an adventure in Venice after the Family of Blood, this is a shippy version of season three and AU beyond that.