Sorry for the double post, but reposting a theory I posted on reddit:
The quirk that can grant quirks is almost certainly called All for One. But what limitations does it have?
One theory that I like goes that AFO can draw out dormant quirks -- so Noumu was genetically thrown together to use this.
I can think of at least two interesting plotlines for this:
AFO activates the quirks Deku was supposed to have -- fire breathing + attraction, if he was not quirkless. The problem is that, why would the AFO user do it on Deku?
The AFO user could force Shouto's siblings to activate their latent ice or fire powers, replicating the ice/fire ability that Endeavor wants -- I could see Endeavor being whitemailed by the AFO user to do things for him this way.
Given that Trueman went specifically to All Might to tell him about AFO, I'm guessing that AM's faced AFO before -- the mastermind is the one who injured him.
Likewise, Shigaraki is going to inherit AFO. He's being set up as the mirror-Deku, story-wise:
Deku: a child but highly mature, has a focused goal and motivation, was raised quirkless, is a completely normal human, has One for All, being trained as the hero to lead the next generation and replace All Might
Hands: an adult but highly immature, has no particular goal and loses motivation when things don't go his way, was likely raised with multiple quirks, an artificial human?, will have All for One?, being trained as the villain to lead the next generation and destroy All Might