That is the side where your truck is to go you can build out on the back side.
Making garage door taller.
What kind of load is the header over the garage supporting.
Usually 4 or 8 feet.
That made my door height two inches taller.
Easy to do and it can solve alot of problems.
Garage door openings are famous for having undersized headers and rotten out sill plates.
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.
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.
Have your contractors figure this in.
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.