Going purple over bright orange red

On an orange base purples tend to look more burgundy/plum/berry toned, they have a lot of dark muted red tones.
So if you are happy with those types of purple, strand test on your current base.
if you want a more vivid or bluer toned purple you will need to lighten your base to at least a dark blonde

Thoughts on using a heavily diluted blue as a toner? I'm wondering if that will neutralize it enough for a more true purple.  I've never worked with an orange this intense before.

Can you post a pic of the type of colour you want?

This is what I've been before and would like to get back to.

If that's the kind of colour you want then you should be fine putting a warm tones purple dye over your current base.

To me that looks brown with a hint of purple, if you use the Deep Purple Dream on your current base it will be a much truer purple than that.
If you want that brown shade you will need to add brown tones, which is confusing me as you said you were worried about 'muddy brown tones'

I think I was more worried about just a brown mess rather than a controlled brown.

I went ahead and washed my hair with my purple shampoo and conditioner and that brought it from a hot orange to more of a copper. Picture doesn't do it justice.

Then did a diluted electric amethyst with conditioner and let that sit for 3.5 hours. Ended up with this.

But then I did the Deep Purple Dream slightly diluted with conditioner for two hours and now I'm here.

The roots are now a dark brown and the rest is a blue purple. I'm curious to see how this will fade and am now researching red based purples or burgundys to get the color I really want. Just took some exploring.

Thank you!