[quote=Diggerton]
In an old RP I was in the GM gave a small portion of the story to a certain person in between each main plot point for someone to dedicate to their own character's subplot. We could do that.
[/quote]
Sounds like loyalty missions in Mass Effect 2 where a major plot point is dedicated to each party member.

It would be good for character development, and I think that everybody has some interesting problem that could come cause the party trouble.