As a **thought** experiment how would these 3 heads on one organism evolve under the current rules of our world (but with fantastic circumstances)? In order to evolve multiple heads in the current science you really only have 3 possible (general) scenarios. 

1. The creature evolved a head then was slowly favored to grow a second head from scratch via selection. This means the heads are not the same even slightly as they have evolved independently. They won't have the same kinds, size, type, function, etc of brain, or face, or anything. This would be more similar to a a creature with a sheep head and a dog head, no 3 dog heads.

2. Somehow a creature mutated and was born with 2 heads right away and this was selected to keep being this way. Having a complex system like a head and brain just randomly be duplicated is probably so unlikely as to again be considered just impossible. 
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The only reasonable way this might happen is if you have a fetal abnormality that results in a chimera of 3 different organisms fused together. But again for the sake of reproduction, only 1 of them will be reproducing so again complications arise. The mutation of chimeraism would have to be favored in general (even when it doesn't results in a fused chimera) and fused chimeras would have to somehow out perform the same number of organisms as independent individual creatures for this crazy fluke to even persist at all.

3. The creature somehow evolved 3 independent brains right from the start. Developing brains is costly so developing 3 similar or identical brains is extremely unlikely if alternatives (and there are many better ones) exist. So this would probably be something more like a centralized brain and the heads are just appendages (like arms/tentacles). This is possible. 
But 3 real heads with each its own brain... again maybe if they evolved all at once? I can only think of sexual selection pushing this forward (like the peacock feathers) because it is otherwise so useless.

So if life follows the general rules ours follows; evolution takes place over a long time, where the best at surviving and reproducing are best represented, there is almost no scenario in which multiple heads would ever evolve.

To have multiple heads be a plausible evolutionary path in their full capacity (3 identical heads and brains) you have to throw out life as we know it. For example maybe a planet where life evolves in seconds rather years, or the method of selection is NOT survival and NOT reproduction.

Either way 3 heads is a fringe case even in the multiverse.


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Expanding on why this would probably never happen anywhere:
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As a biologist I would say that a plausible scenario in which natural selection would favor evolving multiple heads is probably so improbable as to be impossible in any form of life or biology that resembles our own (even in wildly alien environments). I will put to you first the argument about why this adaption is improbable in our current universe no matter where you are.


The reason this won't plausibly happen is because of the way evolution takes place which sets up basic constraints for the population. Some seemingly unnecessary things can evolve if they have a big payoff (like peacock feathers and reproduction), but multiple heads combines some of the biggest no no's in all of evolutionary science and this adaption has to somehow be better than the alternatives to evolve (there were no simpler or better adaptions that could have taken place?). 

The problems in general are:


I) Having an extremely costly AND unnecessary feature. The problem here is that the brain is the most developmentally expensive part of an organism which will negatively impact not just its early development but its entire life by requiring constantly more resources to exist thereby reducing its survivability, chances of making it to adulthood, making it out of the womb, everything. This is true in any environment. So unless there is a massive pay off at the end there will actively be selection towards removing these heads if they ever came to exist.

II) Evolving 3 extremely complex systems is not parsimonious, nor is somehow maintaining all of them. If anything can do the same job but with fewer steps to get there or cheaper, that's probably what happened instead.

III) The heavy resource requirement accrued means the benefits have to be extreme which means the organism cannot adapt well to changes. This means it probably didn't survive environmental changes that reduced food or any of the huge list of things it needed to survive to adulthood. This also means the 3 headed creature didn't exist long enough to develop 3 fully functional heads in the first place.

IV) Many more reasons I unfortunately can't remember right now as I am rusty.

 So the environment doesn't matter so much as the basic contraints of selection. So to realistically make this possible anywhere, the basic principles of life or evolution have to be different. That is the best answer. 

In our universe if you ever really wanted to have these things around, a mad scientist or crazy government organization would probably be your best bet.