The golds to yellow orange fabrics are just beautiful. If you wanted to pick up more in that color family & maybe some browns, taupe or other neutrals, that could look really stunning ... like a summer sunshiny day hanging clothes on the clothesline with the grass beneath your feet.
Or else pick up more shades of blues like another poster suggested.
I don't think I'd go with the chartreuse at all, but if you really want it, maybe add some true yellows & some yellow greens in with it so it doesn't stand out so much. If you go with that, you could do a split analogous color scheme by adding in some blue-violets (instead of the light blue) to contrast the orange-yellow-green blends.