I was wondering if it was possible to have more than 1 application at a time? For example, we would like to create an application for members to become an advisor or officer. Instead of having them create private threads for the officers, is it possible to have two applications up at the same time?

No but it has been asked for and is on Chops list. On the list is Class Based applications but not sure about how Chops intends to handle Rank Based Progression that has been asked for.