You need someone to go in there and look at how the home is structured. Also where the pipes and venting run. If it is a bearing wall you need to put up supports and that can be pricey. If there is plumbing involved then that is another concern.

I suggest you call in a contractor..estimates are free. They can tell you what would be involved with the alterations you have in mind.

Added: Typically bump outs run under overhangs. If it is pushed out further you have to concern yourself with roofing.

Yes, its possible. The are 2 common bump outs.

1 - Standard framed walls on a common concrete foundation
2- Cantilever. A floor hanging out over air space with no visible support from the outside. Perimeter walls framed on top

Either way, extending the bump out is not inexspensive