Have your contractors figure this in.
Making garage door taller.
That made my door height two inches taller.
I removed some siding and and re did the trim on the top of the door and then recovered every thing with aluminum and installed new rubber garage door sill around the opening.
Easy to do and it can solve alot of problems.
Usually 4 or 8 feet.
That is the side where your truck is to go you can build out on the back side.
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.
To raise the opening you will have to remove the header.
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.
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.