can you clarify 2 things please?
do you use 2 yarns instead of just one? Doing the stitch with the double yarn every time?
Or do you knit with one color for some of the stitches and the other for some other stitches? (stranded color work / Fair Isle)
Or do you knit a section in one color, then drop that and knit some part in another color? (intarsia)
and (less important):
do you knit continental style or English style? (which hand holds your yarns?)
it can be a general help to keep the yarn in containers just to keep the coils from dancing around. In an easy scenario you just use paper bags or plastic bags (sturdy, not the little ones from the supermarket, if possible). You can also use cardboard boxes.
Some knitters have beautiful lined baskets or wooden cases...
This will NOT keep the twisting from happening that you create by turning the yarns around one another and turning your work with the yarns attached but it will help already.