I guess it depends what you mean by a "secret society". The Nazi Party has some attributes of a "secret society", there are TLs where the Nazis rule the world.
In American history, the "American Party" started out as a secret society. When members were asked if they were members of the American Party, they would say "I know nothing about it", which led to them getting the nickname "Know-Nothings". There was a brief period in the 1850s, after the Whigs had collapsed but before the Republicans were organized, where the American Party was the main opposition to the Democratic party. In a timeline where for some reason the Republican party is never formed, the American Party might continue to be a major party, even electing presidents. The American Party had a strong strain of racism and anti-foreigner feeling, it is not impossible to imagine a president with these attitudes building an American empire.
Another thought, Organized crime such as the Mafia (if this meets your definition of a secret society) often would interfere with local elections, can we imagine a TL where they were powerful enough to get the White House? Would they then go on to build an empire?
In the 1920s the Ku Klux Klan was a very large organization, with a huge membership. They were even able to gain control of the state of Indiana. A number of events led to their decline, such as when D.C. Stephenson, a Grand Dragon, raped and murdered Madge Oberholtzer, a schoolteacher. Oberholtzer named her killer on her deathbed, and Stephenson was convicted and the KKK almost immediately went into decline. We can imagine a TL where Oberholtzer dies without naming her killer, or otherwise the murder does not come to light, so the Klan does not go into decline and instead continues to be a force in politics, possibly electing a President.
We can also have lots of fun with groups of Freemasons, and so on.
KEVP