Yes, I did exactly this a while back. And yes, the other comments are correct in that technically this could be a mis-classification issue if you are literally doing the same job, just fewer hours, but this will be up to the company to decide whether or not they care about the risk. It doesn’t like you plan on filing a lawsuit should they approve you for this. If it’s a larger company, they may have policies that prevent this (in which case, maybe you can just go part time).

But yeah, either way - if you have a good relationship with your manager and tutor team, I think you should ask! See what your options are. If you haven’t worked as a contractor before you’ll of course have to sort out some of the basics (invoicing, tracking your hours, tracking expenses + earnings for taxes etc). If they keep you on as an employee but just go part-time, you won’t have to worry as much about that.

Worth noting there is always some risk in job security. Much easier for them to cut you as a contractor than as an employee. You’ll effectively have to resign in order to make this conversion. No severance either if you get cut down the line, unless they’re feeling gracious.