Given the full title of The Marvelous Land of Oz: Being an Account of the Further Adventures of the Scarecrow and the Tin Woodman, the sequel, as the name implies, focuses on the adventures of the Scarecrow & Tin Woodman after Dorothy & Toto head back to Kansas. Tip, a new character, is the ward of the Wicked Witch Mombi. After being threatened by her after playing a prank, Tip runs away with Jack Pumpkinhead, a Jack-o’-lantern he had carved that Mombi brought to life with her Powder of Life.
After a revolt forces him to flee, the Scarecrow escapes the Emerald City alongside Tip & Jack. They link with the Tin Woodman in his castle and prepare to go back to the Emerald City to put down the revolt. After some twists & turns, someone does end up on the throne, but it isn’t Scarecrow.
While not as popular as its predecessor, The Marvelous Land of Oz has still lend itself to several adaptations. Some even contend it was written with adaptations in mind; The Wonderful Wizard of Oz had proven to be a massive hit and some details in the book seem to be geared towards the stage.
You can get a full hardcover set of the books here.