How do I bleach black dyed hair without damaging it?

I know I should have thought of this BEFORE dying my hair, but I dyed it black about 3 weeks ago and I want to add blonde highlights. My hair has been bleached multiple times and the ends are pretty frizzy already as I'm growing out the part that was bleached. Even when cut, they frizz soon. Is it possible for my to bleach highlights (enough to be blonde, not too orange) without severely damaging it? Thank you!