Just wanted to point something out here about inks in general.
Most inks are what are called pigment emulsions. That is, is the color (black, blue, whatever) is pigment which is ground very fine and then mixed with a vehicle of choice. Pigments are carried alongside the vehicle, they can seperate over time but will never be one with it. Vehicle meaning, water, oil, acrylic binders, etc. Pigments are not particularly known for their staining abilities. Though there are some that do very well, like phthalo blues (that lovely peacock shade of blue)that darn stuff stains EVERYTHING it touches. Then there are the alizarins, they stain a little bit but are bad about the whole lightfastness thing. They fade really bad in the sun. Dye's are somewhat different as they are designed to stain. They might still be pigment based but the pigments themselves are ground VERY FINE. But most dye is like tea or coffee, where the color itself permeates the vehicle (water, oil, whatever) and they become a new sort of thing. They become ONE with the vehicle.
Synthetic pigments are great at staining. Natural pigments are for the most part not.
On the other hand, natural dyes are great at staining (ever cook some red beets, blueberries or accidentally crushed iris blossoms?)
So in conclusion, if the ink you are using is working and not a lot of discharge after the fact then go for it.
The whole dying something a dark base color before dying it black is a wonderful idea. I use it all the time when I am decorating my cakes. If I were to just use black I would get a dark grey at best and when it fades sometimes it becomes an icky green, or dull reddish brown, but if I basecolor my icing first with blue, or red (depending if I want my black to be warm or cold) then I have better luck with it staying BLACK.
On another note here, I have my best yarn dying results when I use bakery airbrush colors. The pigments are ground VERY VERY fine so that they don't clog the needle which makes them perfect for using as dye in my yarn. Probably not very practical price wise but hey it works. I just have my yarn soaking in vinegar/water and then squirt the colors right onto the wool, nuke it for about 5 minutes and let it sit til the color is absorbed and the yarn is cooled.
Sorry for the long long answer.