It's pretty much what Alternate History is, but I was thinking about some of the real alternate situations we could put historical people in.
For example:
Abraham Lincoln. In a TL where Benedict Arnold becomes the first President, prolongs the Federalist Party's existence and eventually leads to a last minute stand of slavery and a Civil War in the 1840s, Lincoln isn't compelled to stay in the east where he feels he's most needed by the nation. In the 1850s, he accepts an offer to go west and become Governor of Oregon Territory. (I'm on a different computer and this is a VERY rough outline for a TL, so dates, names, and places will change, but it's just the idea) It's commonly believed that Lincoln's move to Oregon would've ended his political career.
ITTL, Lincoln becomes the front-runner for America's increasing contact with Japan and the Meiji War that is breaking out. economic opportunities and political imperialist interests soon back Lincoln in his move to increase Oregon's infrastructure and overall capital. The current President eventually has to respond to some American sailors being killed by honorable Japanese warriors.
The Meiji War now involves the United States allied with Emperor Meiji against the Shoguns. Due to the (Liberal?) Party's handling of the war effort, Lincoln and the (Conservative?) Party are in line for winning the next election (either 1872 or 1876) which they jump at. Lincoln enters the White House under alternative circumstances and an alternate historian would have a chance to examine a Lincoln Presidency that isn't overshadowed by the overall status of the nation.
That was just an example. Feel free to critique, but other scenarios are encouraged for OTL people in ATL situations.