I imagine there are some "legitimate" escort services or ones where the client decides what they want. Even those that are basically a front for prostitutes/gigilos would gladly take someone's money for simply a night on the town.
Even if it were not your intention to offer sexual services most likely you'd have some employees willing to cross the line with clients behind your back in order to earn extra money. Naturally if they got busted you would be arrested as the owner of the business.
Staring a speed dating service or starting your own online dating site are less likely to potentially put you hot water. There's a company in the Chicago area called, "It's just lunch", The company arranges for members to have blind date lunches.