Wall extensions because garage doors are usually sized to snugly fit the dimensions of the garage itself making the door larger usually means making the garage larger.
Making garage door taller.
Garage door openings are famous for having undersized headers and rotten out sill plates.
One way to do it would be to get wall extensions for the entire the garage and then cut the roof of the garage off lifting it up to the height you want it.
Usually 4 or 8 feet.
To raise the opening you will have to remove the header.
What kind of load is the header over the garage supporting.
You are only raising the roof line the studs can be extended by installing say a 6 stud 3 4 of it above the top of the existing stud you will have to remove the top plate and save as you can then re attach it to the new top of the walls double plate included it depends on how your garage was made.
If you have the room on the back side of your garage you can make your garage into what is called a jack jill garage.
Easy to do and it can solve alot of problems.
Have your contractors figure this in.