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Let's say that, given better circumstances; like a stronger showing in the South and Midwest, and/or perhaps earlier NM, AZ, UT, OK statehood, victory in California, and the development of a kind of "Solid West" mentality; the Populists successfully get to the White House and become an established party.
So you have an election something like this:
Could a Populist Party that builds up a "Solid West", a more effective and concrete platform, and wins the White House in the late 19th century survive as a direct third competitor to the Democrats and Republicans without one of them dying?