It could be as simple as adding a new set of recipes (I know, more complex than it sounds, but less complex than some answers).
WVR 19: Fire Shard x1, Water Shard x5 Cotton Acton + Distilled Water + Celest-blue Cotton Dye --> Cotton Acton (blue).
If you wanted to get a bit more complex, you could add recipes that took a colored item and changed to a different one.
In either case, cotton items would still be restricted to (uncolored), blue, green, red, and yellow, the same as now.
If you wanted, you could also add bleach, used to return a colored item to it's uncolored version before dyeing it again.
(there's a possible abuse here, something would have to be done to keep this from acting as an alternate item repair system. Either require ingredients to be at 100%, or carry over damage from ingredients to finished items.)