Of course you can run a side business. I know a lot of folks who are doing just that. I know people who are doing everything from law enforcement to stock trading to owning their own restaurant franchise. I know several who run semi-trucks, one who owns a marina, a few who are into real estate, and several who are involved in flipping houses and general contracting.
What do you want to do on the side? Do that.
Or do that, and fly on the side. Your choice.