Cleveland wins in 1888

As we all know, the 1876-1888 period was noted for particularly close elections (all four are in the first seven by popular vote margin - the remaining ones are 1824 (duh), 2000 and 1960); and honestly, the 1892 one wasn't much of a landslide, either.
And in 1888, the incumbent Democratic president, Grover Cleveland, after winning his party's nomination, proceeded to defeat his challenger, Benjamin Harrison, in popular vote... and badly lose in the electorals.
Well, not as badly as it looks like by the result (233-168) - it actually was just one state. New York.
A state which Harrison won by a percent or so - by fourteen thousand votes.
Of course, Cleveland himself did almost the same in 1884, with a margin over ten times less (indeed, the closest one until 2000 - the margins of 1876 were less in numbers, but more in percentage).
But still, let's return to the original topic: 1888. Cleveland was the incumbent Democratic president, he won the popular vote...
So what if he won the election as well?
What would he do that Harrison didn't? What would he not do that Harrison did? And most interestingly... would he run for a third term - the one that was his second IOTL, in 1892?
Because - I know that might be a bad thing, but still - it'll be totally hecking cool to have a three-term president in the 19th century. And yes, I know it's probably totally implausible, that he will lose in a landslide, that he won't even get the nomination, whatever. But just what would happen instead, and who will be elected president in 1892? And what, by then, will 1892 look like?
Discuss - heck, maybe I'll actually finally write a TL that isn't just a parody of American elections! But discuss anyway. ;)



...So what, how?
January First-of-May
 
I think Cleveland thought about running for a term in 1896. So I would bet that Cleveland would run for a third term in 92. He might have been one of the few Presidents who had a chance at being a third termer.
 
It would set Teddy Roosevelt's life on a completely different course:
if Cleveland is President in 1888, he's not likely to choose TR to head
the Civil Service Commission.
 
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