Is there a way I can dye my hair a brighter red without bleaching it before coloring it?

I’ve been dying my hair for a while. i had honey blonde highlights in dark brown/black hair 2–3 years ago in which the highlighted sections were bleached before so the color would showup. i’ve also had my hair dyed burgundy, more of an auburn red, and now have been dying it a cherry red color with this dye i bought at a beauty supply store(sally beauty supply) i’ve gotten a lot of compliments on it, but would like to try a brighter red(not neon red)so can it be done?