Been there, done that early in my career, and it worked beautifully. The trick was latching onto an established freelancer, someone with their own LLC and a steady roster of clients already sending invoices. When their plate overflowed, they needed a junior to absorb the extra work, and that became my side gig.
The rhythm was uneven, honestly. Busy seasons meant steady money rolling in. Slower stretches meant crickets. What made it work was availability. Late afternoons, evenings, weekends. I made myself easy to reach, so they knew they could lean on me whenever a client needed something yesterday. At my junior salary, some months that extra income pushed my earnings up by nearly half.
After a couple of years, my regular paycheck grew enough that the grind stopped making sense. Free time won out in the end. It's a much easier setup when you're single and light on responsibilities outside of work, though, because those evenings and weekends give up fast.
One big caveat: plenty of agency employment contracts flat-out prohibit arrangements like this. Read yours carefully before chasing anything.