For me, highlighting black depends on what the surface is.
For artificial stuff, like plastic or sci-fi surfaces, grey works. It looks artifical to us.
For cloth, a bit of Bubonic Brown (or any of the pale ochre browns) mixed into the black-grey-white progression does the job. It looks natural, and clothy. It can look more weathered and/or of a poorer quality cloth if you add more of the brown, but just a bit of it can do cloth of quality it looks fine on a fancy noble type.
A blue-grey, like Shadow Grey added into the black-white progression can equally make a pleasent black highlight.
My go-to to method for leather tends to involve a bit of a a rich dark blue (like Regal Blue) added into the black-white progression. It works, as we often see leather rendered that way in arty photgraphy and the palettes of films like Batman and Underworld.
A favoured process incorporates turquoise. As so little in the world is dark turquoise, we don't see it as a dark turquoise but "oh, that's a highlighted black". It can be tricksy getting the levels right with the incremental amounts of black/turquoise/white for the highlight stages. It's easier to use Coal Black fromt he P3 range of paints as it's a dark turquoise already.
Can be prudent to start the highlighting early. Ensuring only the deep recesses are true black. Else, too much is black and without contrast between the shadows and midtone. Though it's a tricky balancing act, as it can all too easily end up not looking black at all, but a dark grey or dark-whatevers-added. I've found it best to ensure there's a lot of tones in around the 1/3 stage between the contrast from black to white, so it's dark enough but has room for highlights to really give the definition.
The surface is of course suggestive of how sharp a contrast you go with too. Something like shiny leather, you want to go with a high contrast, bright white highlights with few stages before the white is on there. Whereas a beaten leather or cloth being a more low contrast surface you can sneak an extra couple of layers in before having the occasional pure white highlights on the extremes.
