More Dominant 36 year period for a party: 1896-1932 GOP vs 1932-1968 Dems

[OSR stands with Israel]

Ill say the Dems as the 4th party system GOP was pretty much non existent in one part of the nation, while the 5th party system Dems could win everywhere.

[Podgy the Bear]

The 1932-1968 Dems--with the peaks at 1932-1946 and 1958-1968.

As mentioned by the OP--at this time period, the Democrats were winning everywhere at the national levels.

The 1896-1932 GOP was also quite powerful, but the Democrats in the South plus NYC provided a strong counterbalance.  By 1928, the Republicans were probably at its peak by making deep inroads in the South--but the Great Depression wiped that out for a generation.