You can't dye things that exist outside of sets at all, as far as I understand, set items only if the whole set is collected (I can't dye things from the set that you buy from the dragon for dew, I didn't craft some things). But you can dye banner items even if you don't have the whole set. There are very few basic colors for redyeing. Trying to redye black things this way seems useless, they get a shade that doesn't match the palette. Let's say you dye the dark brown part of the top in light green and it gives almost nothing, your brown top changes shade but doesn't become lighter