I would also go a few feet taller this would allow for a taller mudroom whose roof would actually clear the edges of my back door.
Making your garage door taller.
That means if you do want to raise the height of your door you may need to raise the roof line of your entire garage.
You answered the question yourself.
The other way involves more work and more money and a most likely goofy looking result with the 3 add on to the door.
Measure the width and height of the door opening.
If your home can accommodate a larger garage door and you d like one make sure to get a track extension kit with your garage door opener.
So if you have a 7 foot tall garage door the depth of your garage shouldn t be shorter than 7 and a 1 2 feet.
If your garage isn t detached and is built within the main structure of your house you will likely find raising the roof line to be either impossible or so cost prohibitive that it isn t worth the investment.
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.
How to frame a garage doors opening in this case 9ft wide by 8ft tall.
How to measure the finished width and height use of 2x4s for the sides and 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.
Maybe go from my current 13x22 to a 15x24.
Knock the garage down and build a new one that is slightly bigger.
The depth of your garage can be no less than 6 inches taller than your garage door.
Divide the height evenly by three.
Cut the legs of the racks a few inches.
Make three panels each measuring the width of the door by the height obtained in step 2.