What do you have?
And what 'look' do you want?
There are multiple ways that people use for highlighting and shading any starting paint and it's largely a matter of taste - rather than right/wrong - which one to use. For some reds just white can work okay, although often using yellow as well works better for reds. Same deal with greens and orange.
For crimson and reds more toward violet just white is usually better (although sometimes the tints are too vivid so you need to dull them down a bit for realism).
The halftones on red (the medium shadows) should still be the same red in hue. Ditto with the darkest shadows, although they're often dark enough that you can't tell if they're a bit off. The commonest painter's way of achieving a duller version of any starting paint or mix is to blend in some of a mixing complement.
For modelling I think that the halftone colour with added black often makes quite an acceptable deep shadow colour, although you may find it too dull. That's where taste comes into it.
Einion