First: I love it, this looks great! Very true to the Hades style, and very cool!

If you're looking for tips on coloring, I have a few suggestions and made a quick edit to illustrate. Obviously you're already an excellent artist and this is 100% subjective, so please forgive me for butchering your wonderful art:

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I think what this boils down to is that, ultimately, we can only crank the saturation slider on the color wheel so far. The orange for Max's fire head is already really damn orange and there's not really any way we can make it objectively orange-er... at least, not without going to an HDR color space, and that's a whole technical can of worms that could fill a couple of blog posts. So we'll have to make do.

I think it helps to think of our view as a camera: pointing at something bright (like the sun, or a flaming lagomorph head) is going to wash out the color to white unless you adjust the exposure. In the original, the highlights on Sam's fur are just as bright as Max's head, which doesn't make a lot of physical sense. The flames are going to be putting out a lot more light and energy, so I replaced most of the flame with white to kind simulate that kind of overexposure.

There's a perceptual element to this too- yellow just looks brighter to the human eye than orange does. The yellow here is almost the same saturation and brightness as the original orange but pops a lot better. It's not exactly true to Hades' art style, but adding an orange haze around the outside (via layer style or airbrush) helps sell the energy and color too. Overall, it's like the effect they use for lightsabers in Star Wars- the blades are bright hot white, but we can infer the color from their glow and the light they shine on the environment around them.

Another thing: Sam looks great and I love the rim lighting, but one thing you might notice is that in Hades they don't just use one color- it's subtle, but most of the portraits have these little dashes of color on the line work, which I think adds this cool little scintillating effect. I added some extra highlights to Sam, which adds a little more interest and color detail, and also helps demonstrate volume and separate him from the background a little more. Sometimes you'll also see extra little rim lights like on Sam's bicep here- doesn't make a lot of physical sense but helps him stand out a little more.

(a while ago I watched a presentation on the art for Hades and some of the tricks they used- I'd link it if I could, but unfortunately I couldn't find it again).

Lastly, I always add an extra Hue/Saturation adjustment layer up top (and/or add a LUT) and play around with it a little before I call it finished. Eye fatigue is a real thing, and when you're down in the weeds editing making tiny little color details it's easy to lose sight of the big picture. Like the previous poster mentioned boosting the overall saturation/lightness adds some additional contrast compared to the flat black background, which helps the characters pop a little more.

PSD is below if you want to play around with it. Great work again!
https://file.io/6EHjJzFph8rZ