In Hollywood, television writers’ rooms are normally seen as sacrosanct creative spaces that are off-limits to business executives. But when writers for the three Marvel Studio TV shows destined for Disney’s new streaming service gather to brainstorm, Marvel Studios production vice president Nate Moore and other executives are often present to ensure storylines remain faithful to the comic book and film universe and, more importantly, the writing process keeps moving.

And they’re not the only company executives weighing in. Disney’s CEO Bob Iger has been personally involved in greenlighting some of the series for the streaming service, according to two people familiar with the matter. That’s a sign of how closely Mr. Iger is monitoring original series production for the streaming service, Disney Plus, on which Disney is betting its future.