Ballet is mired in tradition. Startups are all about changing the things that people never questioned. It's almost an oxymoron to try to run a professional ballet company as a startup - at some point you may have to pivot to not being a ballet company, and then you're no longer a professional ballet company.
I'm not entirely sure what OP's idea of a "startup" or "the next level", aside from taking a regular "small business" and turning it into a "slight-larger small business". However, one of my childhood dance teachers founded a small dance theater (http://toygunstheatre.com/) which seems to have grown in the past few years, so the later is not unheard of.
