The thing to remember is that a work permit and an ARC are separate (this is my thought, of course, not necessarily the view of the nice folks at the CLA). In theory, if you're a garden-variety foreigner (not married to an ROC national and in Taiwan less than 7 years) you would have to obtain the right to be in Taiwan through your official activity (study, work, missionary activities, or visiting relatives). That government recognition of your purpose gets you an ARC -- the certificate that it's okay for you to be there. The ARC itself doesn't mean that you are okay to work, and in fact if you read it there's language that says that the ARC becomes invalid if the underlying work permit stuff is cancelled.
In the past, as I said, I always had one ARC but multiple jobs (each with a letter from the appropriate ministry saying it was okay to hire me for said job). And I always filed multiple (I mean like 8 or 10) lines of income on my tax return, and no one ever said a single word. The only time anyone commented was one year when my income dropped compared to the previous year, and they wanted to know what had happened.