Not sure how plausible this is, but I'll give it the good old try!
Former President
George Hunt (1917-1925 D-AZ) and President Franklin Roosevelt (1937-1946 D-NY): The second vice-President to Woodrow Wilson had served only 44 days as Vice-President before Wilson tragically passed away due to a stroke. As an unexpected successor to Wilson, Hunt followed up with many of Wilson's ideals, finishing WWI in 1918, he tapped many important Democrats and Republicans in Congress to secure entry to the League of Nations (via ratifying the Treaty of Versailles), even contacting former President's Theodore Roosevelt and William Taft for support, and personally meeting with important Republican's on the issue, such as
He got a watered down version in 1919 that removed Article X among other things to placate Senators with Irish and German voting blocs. Come 1920 Hunt would choose James M. Cox as his running mate. With the passage of the 19th Amendment, (and Hunt's past as Arizona Constitutional Convention President who supported women's suffrage), a decent end to the First World War, him and Cox became the first Democrat ticket to win 3 elections since Martin Van Buren in 1836. By 1928 he would lose much favor with his party, especially in the denouncement of the KKK and of black voter suppression in the South. Rather than risk splitting the Democratic Party, Hunt retired to Arizona, where he would meet with fellow
Bryanite and former assistant-Secretary of the Navy Franklin Roosevelt. The 1924 convention was a mess, taking 100 ballots to reach the compromise ticket of William Gibbs McAdoo and John Nance Garner, who would go on to be landslided by WWI Humanitarian Herbert Hoover and Calvin Coolridge.
FDR would go on to be elected in 1936 after the Fast Depression started in 1934. President Roosevelt would model much of his New Deal after both Wilson and Hunt, becoming another Democratic President to die during wartime, this time passing the torch to former Louisiana Governor and Senator Huey Long in 1946
President's:
Woodrow Wilson (1912-1917)
George Hunt (1917-1925)
Herbert Hoover (1925-1933)
Calvin Coolidge (1933-1937)
Franklin Roosevelt (1937-1946)
Huey Long (1946-)
(I've always like George Hunt, and that picture was something I felt I had to use in this situation.)