So like pluck two figures out of history, have them converse with each other (assuming we've got a good translator here), see how it goes?
Napoleon and Genghis Khan. Both tried to take over the world. Would they hate each other? Decide that Napoleon gets Europe, Genghis Khan gets everything else? Want to go fetch their armies and fight right now?
Leonidas and Xerxes I, but in 485 BC. Have a few bodyguards on each side. If Xerxes has this chance to see the Spartans before he launches his invasion, does he still launch it?
Kaiser Wilhelm, Woodrow Wilson, and Tsar Nikolai II in 1916. Put them in a room together for a week and see if they can figure out a way to end the war. Wilhelm and Nikolai should have at least some awareness of the tenuousness of their positions, and Wilson is still leading a neutral country and has probably thought up some of the precursors to his Fourteen Points. You'd probably have to have some French and British and Austro-Hungarian and Ottoman leadership as well, but those three seem like a good starting point, and maybe a smaller group would work better than a larger one.
I might be missing the point (should it only be non-chronologically-the-same figures?), but the "figures who lived at the same time but lacked opportunities to be in the same location" angle is interesting to me for the historical what-ifs. What if you brought together King George III and George Washington in 1779? What if Chiang Kai-Shek or Soong Mei-ling (Madame Chiang) visited the U.S. Congress or U.K. Parliament in late 1937 or early 1938? We've seen in the past year how even short visits to visiting governments can help rally and sustain support for a victim of an aggressive war; would that have resulted in significantly more early western support for China? Could that have also helped make the Nationalists strong enough to retain power after defeating Japan?
