Major visa issues

I am a korean-american and My wife and I are currently in taiwan on a 30 day on-arrival visa (landing visa). We want to start language school at a local university but because we are here on a landing visa" we are required to go out of the country and get a student visa. (because we didnt do this in the states thinking that once we enroll in school, our landing visa will automatically change to a student visa, which was not the case.) Now the only problem is that my wife doesn’t have any more room on her passport for visa stamping as she is on the last page of her passport book.

My question is, can I leave the country with her, get my student visa and then have her under me with a spousal visa while we are going to school? Or does the spousal visa only work for work and ARC’s? Please let us know if you have any information.

She’s going to need a new passport, or at least some extra pages attached to it. I think she can get this through the American Institute in Taiwan (assuming she’s also a US citizen).
Whether she has a spousal ARC (in which case she won’t be allowed to work – not sure about attending school) or her own one, she’ll still need space for a visa of some sort, I think.