Hi! In most countries, if you are not a citizen, you can only work for the person or company who provides a work permit. Recently in Taiwan it has become possible to work for more than one school as long as the hours do not exceed the maximum allowed (something like 38 hours).
Having said that, it is nearly impossible for authorities to regulate tutoring. If you are going to someone's house a few hours a week or meeting someone in a coffee shop for tutoring, how can they prove you are working? Anyway, I have never heard of anyone getting busted for tutoring. I have heard of people getting deported for working at a school that did not provide a work permit . . .
Anything is Legal, as long has you do not get caught.
Sounds cliche, however I know of ESL Teachers that did on the side tutoring, so that they can increase their fund portfolio. It was expressed to me that, as long has you do not get noticed etc, they usually turn a blind eye, and the secret was to be stealthy about it.