How to overdye super saturated blue linen?

I bought a set of 100% linen duvet and shams online on clearance. I was hoping from the product photos that it would be more slate blue or purple leaning than dark indigo.

I would like to change the color to a more purple tone or slate tone. I think the purple might be easier to achieve. I am thinking of using a dark purple dye like Dharma's Fiber Reactive Procion Dyes in either deep purple or ultra violet to produce a purplish effect. I hope to just shift the color to something a little less indigo blue.

I have included photos of the same sham both outside, in direct sunlight and inside, in indirect lighting for reference.

My questions:

1. With how saturated the color is, will overdye have any effect?
2. Should I be using a similar level of color saturated dye?
3. Any other advice this wise dye community can offer?