This theory has been brought up before, but I have a slightly divergent outlook on it. I haven't looked at theories in-depth so it's possible I'm regurgitating the theory of someone else; should that be the case, sincere apologies!
How Many Is Blackbeard?
First of all, there's a scene with Luffy & Zoro (along with Nami) listening to Blackbeard's speech about; bare in mind that none of his comrades are nearby as far as I can see in both manga & anime. Nami's response after this speech is who is he? Yet Zoro and Luffy reply it's not "he", it's "they".
Now, it doesn't even matter if his crew was there, it's a very odd reply to say "they" when she was enquiring about this particular fellow's identity.
She wasn't interested in him & his crew (if they were even around him) but he himself, nor did they (apparent crew) even add to his monologue to justify accounting them into the equation.
The whole focus was on him and no one else, so it's very unlikely that "they" is including the people around him.
What's even more interesting is that they correct Nami's query and change the "he" to a "they". Also she asks if he had companions around with him to justify the use of "they", so that means she didn't see anyone with him and he was the only person there.
One has to conclude that he's not just 1 individual, but 2 or more individuals.
Marco also comments on Blackbeard saying the make up of his body is different to normal humans and questions if that's why he's able to take to Devil Fruits; that scene also goes on to confirms to the readers that it's impossible for humans to handle more than 1 fruit as an absolute fact.
So prior to eating any fruits, Blackbeard's body has always been different. His body composition makes him synonymic to multiple individuals rather which is at least 2.
Just to add, knowing that Oda loves to make references; wouldn't it be interesting if Blackbeard was 3 people referring to the trinity which is a common concept in many different religions. Fact that he has a "Jesus" in his crew may be hinting at Christianity?
Acquiring DFs
We know that you need the fruit that's related to the DF at the very least when trying to acquire a DF from a dead person. It seems this is pretty common knowledge as Doflamingo was able to acquire the Mera Mera No Mi.
Although, despite having this knowledge, it still comes down to sheer luck; the only example of acquiring a fruit that worked without a cinch was Sara Sara No Mi and we're yet to fully understand how that worked.
Perhaps knowing the fruit is key; in acquiring the Sara Sara No Mi all the fruits in the basket were apples, so Caeser must have had knowledge of this prior to this experiment.
If that's not the case, maybe DFs change the fruits they reincarnate into; Smiley was an artificial DF after all, so perhaps it was engineered to always reincarnate into apples; assuming this randomness is true, it would make extracting DFs still problematic and depend on sheer luck despite any knowledge.
WB and Ace died in the same place, yet Blackbeard had to wait till he heard news about the Mera Mera No Mi before venturing to acquire it through Jesus Burgess. This implies there are still limiations in extracting DFs from dead people except you have the Yami Yami No Mi (which I'll move on to shortly)
The bag with Burgess possibly contains multiple fruits to increase the chances of getting the DF of his choice except he knows what fruit it's going to spawn; I'm inclined to go with the DF's fruit of choice is always different to the last or it'll be too easy.
Yami-Yami No Mi
The Yami Yami No Mi absorbs everything, it's simply because of this fact that he was able to guarantee absorbing the Gura Gura No Mi; without this DF, he would have had to search for it or wait to hear news about it appearing to obtain it. Had this not been the case, he might have brought a bag of fruits to obtain both Ace's and WBs DF had anything gone wrong.
In conclusion, the Yami Yami No Mi guarantees him the fruits of his choice and doesn't nullify the inevitable death that comes with trying to consuming 2 DFs. Anyone else with (or without) the Yami Yami No Mi who attempted to do this would probably die if they didn't possess a similar body to Blackbeard.
What's even more of a mystery is why is Marshall D. Teach is possibly the only one with a body like this? Are there more people like him? Is he the result of an experiment? Or is he the only survivor of a race that should have been extinct from the "Void Century"?