Need some help. New addition, designing the roof.

The roof would get raised to the needed height to compensate for the addition.
The plans you would get to give to the building dept would give you the visual and the methodology. You will need plans to persue this. Have you spoken to an Architect?
Ron

Are you doing this work yourself?
Where are you located?
How big will the bathroom be?

Yes, doing all our own work. Live in an extremely rural area. No city or county regs or codes.

I've worked residential construction for nearly 25 years. House building/framing in my younger years. Just not sure how to go about tying into a valley. Can I just go up the roof on the right side at a lesser pitch, then create a new valley on the left side?