Yes, it's completely possible. You need to make sure you use a needle with a blunt tip, and then make sure you only weave the yarn through the 'gaps' in the existing stitches, not through any of the yarn itself, because that would snag and stop the new yarn sliding through cleanly.
use the needle they sew jumpers up with once knitted, it has a blunt point and the eye can easily take wool/yarn it will be much easier than using a crotchet hook, you will make the existing yarn stretch and pucker doing that
You can do this with a suitably sized crochet hook, and follow the loops of the knitted garment, using a simple chain stitch, or you can use a large eye embroidery needle and weave your yarn through in all sorts of designs...I once made a stallion rearing on a cream chunky jumper by this method, first I tacked the main outlines in bright thread, to be pulled out later, and then filled in with all sorts of shades, weaving ends into the back of the work, it looked amazing..gather together lots of scrap wool to give you loads of choice..