I have a friend who has just knitted a great cardi in an awful pale lime green 100% merino (gifted to her by her MIL)... Now, if said friend looked good in pale lime green, she'd be very over the moon about the cardi..
After the obligatory photo to show the MIL, she'd like to dye it to a darkish brown (I'm guessing a chocolate colour).
I'm not sure that food coloring is a whole lot less "chemical" than regular dye -- it may be edible but that just means the dyes in it won't kill you if you ingest them; it doesn't necessarily make them "natural."
Your friend can probably dye her sweater some shade of brown with coloring made from black walnuts, onion skins, etc. Google "natural dyes" and you'll find lots of information.