Semi permanent dye on dark hair

I have medium brown hair that I have been dying auburn for years. I like the way the color turns out but am wondering if I could get a similar result without the damage. I realize this kind of dye is not intended for dark hair and will only give a tint of color, but thats all I want. Worst case scenario I overpay on a deep conditioner.

Could anyone suggest a brand/color? I like a copper leaning auburn and not so much red. I'm open to any brand as long as its not super expensive.