Never done it myself, but I hear it’s easy. In dyeing terms, it’s kinda easy to accidentally dye many black just by overdyeing them - so doing it intentionally ought to be as simple as using black Rit and being patient.
by way of more info on the blurple: I have seen some people get around incompatible color issues like this by dyeing one color first, and then another. If you dyed the orange red, then in the right shade of blue, and did it just right, you’d probably get a nice purple. But it’d be a much warmer purple, on the opposite side of the range of purple colors from Spydie blurple which is a cooler purple, pretty close to regular indigo.
To forestall what may be an obvious question: if you dyed it red then actually used indigo, instead of blue, for the second dyeing, I think it’d just look dark. Not purple, but also not black. Pigments eat a lot of light, so you have to account for darkening when you double dye.