NO. Runaan's isn't weak, it is niche. Get the difference? If you did this, champs that already use it would become stupidly over powered (Kayle, Teemo, Kalista, etc.). Can you imagine a Kayle hitting you for the magic damage of her E+Nashor's Tooth three times per attack? What about Teemo, toxic shot+Nashors three times per attack? Kalista getting 9 stacks of rend in three attacks would give absurd burst. Varus blight stacks maxing out in one shot would give him over 15% max health damage per attack if he popped the mark in between attack!
This doesn't make the item any more appropriate for any other champions, and would only break the champs that already use it.