Cel shading uses two shadow steps
The basic anime look stacks a first shadow (soft) and a second shadow (darkest) over the base color. A highlight where the light hits adds volume.
Shift the hue instead of adding black
Mixing black into a shadow makes it muddy. For skin, shift shadows toward red or purple; for cold scenes, toward blue. The shadows look clearer and more alive.
Make line art from the base color
Instead of pure black, use a darker version of the base color for line art. Skin lines in reddish brown and hair lines in a deep version of the hair color blend better.