Well, see topic.
Trajan died at Selinus in 117 after suffering from the heat over the last year, but he always saw this as just a temporary illness and was setting out to take care of Jewish revolts. What if he was right, and recovered?
Someone of his ability would have taken care of the revolts quickly (Hadrian did so, if I remember rightly), then move back to his previous tasks. I've heard that he had crossed into and took out the region of Atropatene and the city of Susa even if he didn't convert them to provinces like he did the Mesopotamian lands and Armenia, and I have to wonder if he'd then move on again and establish even more of Persia to be Roman territory.
That's probably my big wonderance and divergance: would these areas he conquered STAY Roman? Would Rome, delayed by the would-be Emperor Hadrian's tours and peaceful reign continue to conquer new lands for a bit longer and consider itself glorious for doing so?