Though each condition will be unique and you should consult with a qualified professional before undertaking any project such as this, here are some general tips and tricks for building a cantilevered micro-addition.
1. The simplest approach is to "sister" new floor joists along side the existing joists. This can be done with minimal damage to the room below.
2. Depending on the roof condition and how the micro-addition is designed, you could end up with a lower ceiling in the added area. This could be a good thing, especially if the added area will be used for a featured element like a spa tub.
3. In this generalized sketch, the existing roof slope is continued to the new outside wall. This doesn't have to be the case. There as many ways to design this roof extension as there are types of roofs.
4. Using a cantilevered micro-addition to expand a kitchen or bathroom can be a great way to get that extra space to have that spa tub. However, make sure that no water pipes or plumbing lines are installed in an unheated space.
5. A cantilevered micro-addition on an existing second floor also can be used to add space to the room below. Rather than supporting such a niche from below, it can be hung from above.
Again, and this can't be stressed too much, make sure to engage a qualified professional before undertaking any project like this, and make sure you adhere to local codes, ordinances and regulations.