Can I buy a round trip ticket from Tampa to Tokyo for two months and spend the second month in Korea?

Okay, here's a big question for you. This summer I'm going to spend a month in Japan and a month in Korea. I'm wondering if it would be possible to book a round trip flight from Tampa to Tokyo for two months, buy another round trip ticket from Tokyo to Seoul, spend the second month there and just get back to Japan before my flight back to Tampa leaves. I dont want to buy three tickets because I'm on a budget, and this is my first overseas trip, so I'm wondering if this would even work. I know you have to have proof you're leaving the country.

Asked by Kia via Travellr.com