How to add a room in garage but keep garage door and add new ceiling that doesn't touch existing ceiling

I’m finishing part of my garage as an in-law suite. The garage is 24×24 ft with an 18ft wide garage door. I want to keep the garage door operable and still use it for storage, which mean the finished space would be 12×24 ft. This makes the finished space really tight for everything I want to fit.

I want to bump into one part of the unfinished garage space to create a 7×9 ft spot for a bed and nightstand. I would use one existing wall but need 2 new ones. However, the ceiling of this bump in can’t be attached to my existing ceiling because it would block the garage door. I have 8 ft from the floor to under the garage door support brackets.

Will the ceiling of the bump in be able to be supported by the 1, the existing and 2, the new walls?