Maybe in 1924, if the Farmer-Labor party is in a stronger position, the various progressive factions decide to run under a Farmer-Labor ticket, rather than form a united Progressive Party. It helps give them a significant boost in the public eye, and after the election a significant number of progressives decide to continue to support the Farmer-Labor Party so that it remains a fairly significant third party until the depression hits which gives them another significant boost to their popularity. Finally, Huey Long backs the Farmer-Labor Party as a spoiler candidate to prove that his Share Our Wealth program has potential and ensure a Republican victory in 1936, with the long-term goal of securing the Democratic nomination in 1940. As a result, after Huey is assassinated the Farmer-Labor party is able to inherit a significant portion of the Share Our Wealth movement, giving them significant gains in the rural south.
In addition, the rise of a considerably left-wing party is likely to mean that civil rights is going to be put on the agenda a lot earlier, which is going to cause internal divisions in the Democratic Party.