a predictable response, but it's the wrong one which will surely lose your company plenty of money and valuable employees extremely rapidly while generating a tremendous amount of ill-will from the people in your network. really, it's the attitude that's creating the problematic and unprofitable approach here. aside from being disgustingly invasive and utterly reprehensible from a social perspective, you've also put yourself in a position where you're spending your company's time on something that will never generate it any financial returns, only more costs when the employee discovers your snooping and inevitably ditches you and you need you find a replacement on short notice.
the correct response here is to re-evaluate how much you're paying the employees that are moonlighting because it clearly isn't enough to keep them appeased, which means that by definition it isn't enough to keep them operating at 100% during the hours you expect to be getting 100% of their energy and potential for productive output. in other words, moonlighting employees need a raise because at the salary you're paying them, they know they can't afford to stop looking for more opportunities to work for pay. when you do find a reason to give that employee a raise proactively, you'll increase their output to the level you thought you were purchasing with the initial salary negotiations. you'll also increase their loyalty to the company, and avoid intruding on their private life, which is explicitly, irrevocably, and unimpeachably beyond your purview, consideration, or examination under any conditions whatsoever.
in a nutshell: focus on things you can change, then stay in your lane.