I went to the Osaka Regional Immigration Bureau to get a multiple re-entry permit. I now can come in an out of Japan as many times as I need over the next three years.
You'll will note that the sign is in three languages Japanese (top and only Kanji characters so probably reads the same for Chinese), English (middle) and Korean (bottom). It seemed that most of the other people visiting the immigration office that day where from Korea or China, and I was one of three people there who were from elsewhere.