Is There a Way to Thicken a Narrow Nose?

It is challenging to correct a narrow nose, but this can be done so with spreader grafts and/or other procedures, however, one needs to see and analyze the patient and should be done by a Rhinoplasty Surgeon.

Modern rhinoplasty techniques can effectively widen the nose. The area that needs to be widened will dictate what techniques are used. Often a high bridge or dorsal hump causes the upper part of the nose to look to narrow. Lowering the bridge or removing a hump will widen the nasal bones and make the bridge appear broader. The nasal bones can also be surgically broken and rotated outward to increase the width. If the middle portion of the nose is too narrow, spreader grafts can increase the width of the mid-vault. Finally, a narrow tip can be widened with cartilage grafts.

In some ways you are considering a augmentation rhinoplasty.
This is traditionally achieved by addition of grafts harvested from the septum, ear or ribs.
Some physcians use fillers to achieve a non-surgical rhinoplasty but this is controversial.

Yes. Reverse osteotomies have to be employed where the nose bones are widened, and then spreader grafts are placed in the new location, both in the cartilage and in the bony area of the nose. The tip can also be widened with structural cartilage grafts to create a more balanced, wider nose.

In primary rhinoplasty, it is much more common to reduce or narrow a nose than it is to "thicken" a nose, but it certainly can be done. The middle of the nose can be augmented with grafts (such as spreader grafts, dorsal onlay grafts, or sidewall grafts.) Nasal bones can be moved out to widen the nose. The best thing for you to do is see a rhinoplasty surgeon, and discuss your goals with them. They will let you know if your desires are achievable, and what needs to be done to attain the result.
Good luck!