Bob Iger only left the building at Walt Disney Co.’s headquarters at the end of December, and his successor as CEO, Bob Chapek, is already doing things differently.

In the months since Iger’s departure, Chapek has developed plans to launch a cheaper ad-supported version of its flagship Disney+ streaming service and has explored partnerships for ESPN in sports betting—both of which Iger had resisted. This week, Chapek made headlines when he sent a memo to employees defending his decision to stay silent on a Florida bill that has been criticized for discriminating against gays. Some former associates of Iger—who tweeted his opposition to the Florida bill last month from the comfort of civilian life—believe he would have spoken out against the legislation had he still been running the company.

And Chapek’s next move may put further distance between his philosophy and that of Iger. Disney is exploring the idea of significantly broadening the content on Disney+ beyond the strict family focus Iger favored. Executives have even talked about whether Disney+ should offer movies and shows from the horror and thriller genres, a once unthinkable move for a service closely identified with its kid-friendly Marvel, Star Wars and Pixar offerings, according to two people familiar with the discussions.