Can I work as an ALT on the status of residence I already have?
Whether an existing status of residence permits this work, and whether separate permission is needed to engage in activity outside it, is decided by the Immigration Services Agency. Nothing on this site settles it, and an answer that turned out to be wrong would be the reader's problem and not this site's.
The Immigration Services Agency answers this directly, and a certified administrative scrivener (行政書士) advises on individual cases.