Purple fringing shocker !
If you want less CA...use a better (more expensive) lens that has less CA to begin with. But most lenses will have some...esp in any high contrast area.
The 24-120/4 is already very expensive. At over $1200 new, it's about the same price as the Tamron 24-70/2.8 VC.
But if you really want to see purple fringing, I suggest trying the pre-G Nikon 50mm f/1.4 (either D or non-D version). Shoot it wide open outdoors, and there'll be more purple haze than you ever thought possible. There's so much of it that it actually affects the color balance of the image.