Isn't that basically what flash points and ops are? Where 2 emporers hands a few Agent 9 and a few Darths come together to do an avengers Assemble style story. Which ultimately has very very little story and far more generic content.
Yes, that is very generic, but what I'm thinking is actual class story overlap....think of all the NPCs you have come to know in your class stories. Some are more constant than others (The Watchers and Keeper in the Agent story, for instance). It's hard for me to imagine the stories not having those characters at all. I kind of like the idea of doing a quest where you literally require one of each class to complete and not as much based on combat roll. I suppose some people would not like that idea.