I'm clear that at 9 years old two classes a week at school are enough if the kid is actually into the language. The thing is that "doing okay" can mean a lot of things: does he struggle to pay attention, is he bored, or is it just not his priority yet? That changes everything. If it's real frustration, a private class can help unlock things that don't flow as easily in a group. But if it's because other parents do it and you're scared he'll "fall behind", that's just pure panic.
What works better in my experience is trying other options before dropping money on classes: English movies or shows he likes, online games with other kids, audiobooks, whatever is kind of fun. At that age intrinsic motivation is 100 times more important than an extra class. If after a couple months you see he's actually struggling and is motivated to improve, then go find someone. But if you're doing it just because "everyone does it", you're probably just throwing money away.
One thing: make sure if you hire someone, it's someone the kid clicks with and it's not just boring grammar repetition. A mediocre private class is worse than nothing. And honestly, if his school teacher says he's doing "okay" but doesn't sound the alarm, it's probably not urgent.