True enough, the core profile module does not allow multiple profiles per user.
There may be a contrib module or two which will allow this. Alternatively, there are other ways do this. One could create a "character biography" content type, possibly using CCK depending on how structured the biography needs to be. Then all of the character biographies posted by a user would automatically belong to that user, as with normal node behavior.
I believe there are also a few contrib modules which allow creating user profiles as nodes and similar things which might also provides features which may be useful. Take a look at usernode and nodeprofiles, for example.
..chrisxj