Different stage for each character

[Sonic Boom]

When it was 2008 (I think) I thought about that: each character have his stage.Mean if you play with woody you will have a story of woody,but if you play with davis you will have a different story in stage.
I didn't know about stories in stage and I had an imaginary LF2 with:

Vs Mode
Stage mode
character stage mode (I never found a name for that)
1 on 1....


Now,as I know this can be realized in normal stage mode,maybe with stage chose.
Maybe it is very hard to create story stages for each char but,just for 5 heroes,while other heroes and other characters can see "unauthorized character ".

What do you think about that?!

Yeah Its really a good idea!
But, wouldn't it take too much of time for loading the game?
And Why are you only saying about 5 chars there are 9 heroes I think so the remaining 4 will be kinda isolated from the story.