Since your hair is already dyed dark, you should reconsider using a semi permanent dye. Permanent color doesn’t mean it’s actually any more permanent, it just means it lifts the cuticle when it deposits. The blue tone in a permanent color isn’t going to last any longer than the blue pigment of a semi permanent, and because you’ll have to keep redoing it to keep it looking blue, it’ll add way more damage. Eventually, this will cause it to fade even faster. A semi permanent color you can just keep topping up.

The brand Adore makes a great blue black color, or you could just do one of the dark blues from manic panic or punky.  Punky and Keracolor both make conditioning treatments you can use in the shower to add more pigment to your hair, or you can mix a semi with your regular conditioner.