This one might seen weird and out of nowhere, but what if Blackbead is also a descendant of the Three-Eye Tribe like Pudding?
1– He always has something covering his forehead (and keep in mind Pudding could hide her third eye with just her hair), we literally never saw Blackbeard’s forehead completely.
2– Pudding had some type of multiple personality disorder, that was very clear when she gets confused about her feelings for Sanji. A common theory about Blackbeard is that he has 3 different personallities (or souls), what if the multiple personalities thing is a characteristic of the Three-Eye Tribe people?
3 – Three-eyes possess the potential, with their third eye, to achieve “true awakening”, which supposedly comes with the ability to hear the “Voice of All Things” — thus giving three-eyes potential to decipher and read Poneglyph writing. It wouldn’t be that far of a stretch if they also could consume 3 devil fruits, maybe Pudding just don’t know she can do that yet, or maybe it requires said awakening, which in this case Blackbeard would have.
It’s stated by Oda that Blackbeard likes to study history, if he really has the power of the Three-Eye Tribe that would be quite easy for him to collect a bunch of information, since it appears that they can use some sort of “Voice of All Things” power.
*Theory by Shedinjask