Arts administration! Theatres are run by teams of people who produce, educate, and facilitate the shows they put up. They are best served by people with a knowledge of the art form and organizational skills - my degree is in music and I worked for an music nonprofit for four years and absolutely loved it - it allowed me to use my degree in so many ways I never expected, and I have many friends who work for theatres with MFA’s in Musical Theatre. Options within arts administration include education, production management, marketing, fundraising, producing, and more!
Bridget recommends the following next steps:
On top of that, there are roles like theatre managers, fund raising, box office managers, booking agents, hospitality...
Now, that's all only within the theatre world. Theatre people can make excellent public speakers, teachers, politicians...much of the training you get in theatre can be applied to other areas. One of my friends went into video production. One went into finance. Several went into Information Technology, working their way up to managing very large projects. Some of these fields required additional classes/training, but the theatre background comes in handy in just about any profession.