Hi, I actually joined Forumosa because I googled this question and saw a post on this site about it, but it was a few years old.
I am teaching with an ARC and also am doing freelance writing. I have recently begun doing voice recording and they want to apply for a work permit for me and tax me. I am worried that I am not allowed to do this but cannot find an answer to this question on any of the government sites. The pay is lucrative and they don’t really want to have me work under the table as the fines are so high now. I’m not worried about cops coming in off the street and catching me in the studio, I’m worried about applying for the work permit when I already have one. Any advice would be much appreciated.
Cheers 
littlewing ^,^
If they’re able to get an ARC/work permit for you, then go for it. The worst that can happen is it gets denied, and then you can just continue on as you are now.
Forreigners can hold several work permits, not only the one which their ARC is based on. Your “sponsor” of the workpermit which bases the ARC needs to know and agree to your side jobs but besides that there are no other problems comming up from that. Also, just to apply doesn’t mean you will get it but more than not grant you one can’t happen. At least that’s what they told us from official side.
Apply for the permit before beginning (or admitting to beginning) the work. There’s nothing illegal about applying. It’s only illegal if you start the work first, before applying. The CLA does check tax returns and busts people for this kind of stuff, btw.
You might want to make sure that you are not violating the terms of your teaching contract though. Some contracts state that a teacher may not teach at another school or work privately without first consulting with your schools management.