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Per the Avatar: The Last Airbender bible, which was partially posted here, no. Only the Avatar is capable of bending more than one element.

A bender's powers cannot extend beyond his native element. (a Waterbender can only bend water, a Firebender can only bend fire, etc.)

Further, the The Legend of Korra episode Beginnings indicates that humans could bend more than one element, with the assistance of the spirit Raava. However, due to her merging with Wan, and the lion-turtles who granted bending to humans leaving the physical world for the spirit world, no one except the Avatar is capable of this feat. (there's one likely theoretical exception though, if someone who journeyed to the spirit world and worked with Vaatu, they might manage to gain control over multiple element bending)

During Aang and Korra's time no, only the Avatar can bend more than one element. It has been explicitly stated in the show and by Bryke. Children of 2 different bending backgrounds can produce offspring that bend either element, or possibly none at all. Also, children of non-bending parents can have a bending child. They tend to be withing the same element as their culture, but as we see with Mako, Bolin and Aang's children, that is not always consistent. Also, Bryke have intimated in panels that the element available to the bender is both tied to their personality and informs their personality. Specifically that airbenders access to the element air is tied to their spirituality and that they are drawn from the other three nations. Events in Book 3 may support this interpretation, or could be a one-off event as the aftermath of events in Book 2.

The Avatar's ability to bend more than one element comes from an outside force that is revealed during book 2 of Korra.

As we learn in Korra Book 2 chapters 7 and 8 that bending was granted to humans as a defense against the spirits by the Lion Turtles last seen in Last Airbender Book 3 chapter 19. In the episodes of Korra we see that contrary to local legends the bending ability was granted to humans by the Lion Turtles. With the assistance of the greater spirit Raava he was able to contain the power of air-bending as well as fire-bending. With Raava's continued assistance he was able to learn the bending of all four elements, and his joining with Raava started the Avatar Cycle.

This does not actually contradict the legends of badgermoles, the moon, flying bison, and dragons teaching people how to bend. Though they were not granted the power by those species it is entirely possible that those species taught them how to use and perfect the use of the elements.

As explained in the answer to the question you linked, there are several reasons why someone can't bend multiple elements, and these apply as much to your question as that question.

In particular, even if the techniques to bend sand are more similar to the techniques to bend water, sand is still a variety of Earth, and as such the spiritual connection to sand is formed by Earthbenders, not by Waterbenders, and a Waterbender won't be able to bend sand.

The closest anyone who isn't the Avatar could come to blending an element beyond their own is most likely mixed materials, such as Mud for a Waterbender (due to the high amount of water in mud.)

Finally, as also said in the answer to the question you linked, if it was possible, people would have. Several people in the series are very powerful in their element, and would have grasped the chance to bend another if they could have.

Well bending seems to be a talent a gene they get from their parents, like how some people can sing while others try but no matter how hard they try they cant ever be a singer like the natural talent, plus the Avatar is blesses from the spirits an opening of all chakras, he possess these as well where others do not. Not to mention the Chi needed to bend certain elements, that's why when someone blocks their Chi they cant bend I believe the Chi and the element have a certain connection and like what I was saying earlier about the genes, they could have like a dad who has a brunette gene and a blinds gene Bb, and the mom has two blonde genes but half of those kids will be brunettes and they may have the blonde gene but only the brunette shows well that's what it is for bending I think even though you have the genes of both only one shows

I agree with most answers, but I'll try to offer an alternative one.

We learn from Wan (in Beginnings, part 1) that originally humans would gain bending powers from the Lion Turtles. The granting of such powers was temporary, though; humans received the power prior to venturing into the wilds, and would have their bending removed upon coming home. Moreover, each Lion Turtle would grant only bending associated with one specific element.

Wan subverted this by sneaking into town, so the fire Lion Turtle wouldn't remove his bending. Long story short, he kept his firebending ability in a sort of "permanent" form.

Later on, he requests the power of air bending from the air Lion Turtle. The following conversation ensues:

Air Lion Turtle: You already carry the power of fire. No human has ever held two elements at the same time.
Wan: I'm not like other humans. I can learn to do it.
Air Lion Turtle: Hmm, perhaps. But to do so, Raava must hold the power for you until you master it.

The dialogue is somewhat ambiguous in that it doesn't tell us whether Raava's help is a requirement for a human to hold multiple elements, or if Wan needs her involvement only because the Lion Turtle wants so.

Enter Vaatu and Unalaq.

I won't enter a discussion whether Unalaq's ability to corrupt spirits was an extra form of bending, granted by Vaatu. I am more interested in their eventual fusion by the end of the second season of the Legend of Korra.

Vaatu saw that he was defeated by the fusion of a human and the spirit of light. He then joined with Unalaq to become the "dark avatar". If we consider for a moment that Vaatu's nature is similar to that of Raava, he would be able to hold powers other than waterbending for Unalaq. And while the pair would probably have a hard time convincing a Lion Turtle to grant them more powers (or even finding a Lion Turtle, for that matter), the ability to "hold" more than one element would remain.

So we have one or two ways in which someone other than the avatar could bend more than one element. It has always been a possibility, despite never having happened.

Very intersting question, but the answer reamains a very blunt no. Here's why.

"Only the avatar can master all four elements' this has been stated more than one can count. Considering that none of the avatar had anything in common besides their devinity, it is safe and not illogical to assume that the avatar is merely the incarnation of a spirit among humans. He avatars sole purpose is to kep peace and ballance amongst the nations and thus the world. So the sole difference between say, roku and zuko, is that zuko is a natural born firebender where as roku is just a spirit in human form. What way to keep peace than to istill someome woth ultimate power right? So, base on the rules of the show no one person can bend more than one element unless that person happens to be the avatar. Now, remarking on what followed. There are only four bending elements. Water, Earth, Fire and Air. However, each art has a sub bending dicipline. Water has healing, plantbending and bloodbending. With healing, water benders manipulate the life giving properties in water to achieve healing. With plant and bloodbendig however, the bender isn't actually bending the plants or blood, but the water that is in them. Earth has metal bending and seismic sense and metalbending. Seismic sense is achieved by tuning into the vibrations passed through earth to sense objects far away, or in Toph's case, unseen. Metalbending is achieved by isolating the earthbased impurities in metal amd manipulating them, not actually bending the metal itself. Fire has combustion, lighteningbending and heat manipulation. Firebenders, although never explained, can produce lightening most likely due to the fact that both can only be produced in oxygen rich areas. why they lock firebenders in freezers. Cold air is caused when atoms are far apart and not rubbing past eachother causing friction which in turn causes heat. And combustion can' only be achieved when atoms are overheated, hense why it is speculated that firebenders can control tempature. Airbending has no confirmed sub bendimg art but it has been specualted that if there are any, tje would be weather and sound bending. I added this jist to point out hat a bender can ONLY bend theor natuaral element unless of course they are the avatar. I would like to point out as well that though amon wasn't actually spirit bending, he feet could be acieved by anyone seeing as the art existed before the avatar, even before the four bending elements themselves.

No. Because once you start to learn one element your chi is blocked into that element and cannot bend any other, only the avatar can unblock this chi and learn the other 3 elements. Hope this helped.

No it's not possible the lion turtle told wan that no human has ever had more than one element and the reason being is that thier bodies can't handle it. That's why wan needed raava to hold the other elements if you notice wan never fought with more than one element until he fused with raava
When he fought vaatu he only used fire until him and raava fused

The Avatar is the spirit of the earth in human form existing for the maintenance of balance among the four nations. That is the reason why he can bend the four elements while others can't.

Airbenders learned their bending abilities from the Skybison. Earthbenders learned how to bend earth through observation of the Badgermoles. Firebenders learned to manipulate fire from the Dragons. Waterbenders learned their bending form from the moon.

Based on these facts, I see no reason why someone cannot bend, though, maybe, not totally master, two or more elements.

Here is my reasoning: All of the bending forms were learned, not inherited. Because of that simple fact, there is no reason to say or think that one cannot simply learn how to bend another element from another bender who manipulates a different element, or from the sources the original benders learned their own. An example of this would be Toph Beifong. I'm not sure that it is actually mentioned in the show, but the wikia page on the Avatar series says that Toph learned Earthbending from the Badgermoles. I'm not sure how she could have done this, based on the fact that she's blind, but somehow, she did. (I'm not saying it's impossible that this happened, but being that it never said she knew how to sense vibrations and use them to get a sense of the enviorment around her, I have no idea as to how she actually did it. Regadless of that, her abilities were learned and not inherited, which begs the question: If she learned one kind of bending, why can't someone else learn how to manipulate that and another?)

DNA cannot, and I'll put emphasis on that, CANNOT, be brought up when talking about the Avatar, or really anyone else in the series. The chances of having the same DNA as someone else on Earth are one in well over 6,000,000,000,000. If DNA were a factor in the series, which it obviously isn't, then the Avatar would almost certainly never exist in any point in time, making him seem like more of a god to others.

While I do accept the fact that no one can master the four elements besides the Avatar, it never explicitly says that there is some reason why no one can have a handle on two or more elements. The answers that the majority of you people are giving are totally pointless. You're only reitterating the fact that no one can MASTER the four elements, but have given virtually no insight into why someone cannot at least manipulate more than one element, rendering your answer to the question null and void.

it may be possible for someone bend more than one element because in the new episodes of korra the first avatar learned bending for the land turtles. People at that time use the elements as a defense but never truly mastered it or used it as an extension like Wan the first avatar and they could only borrow the power of the element and return it . Wan was a fire bender at first he then trained with spirits for a short while and then traveled and met 2 spirits. The spirit of lightness was fighting the spirit of darkness the spirit of darkness tricked him and told him the light one was bad and was tormenting him. So Wan help him get free and then the dark one left spreading darkness through out the land. So wan went to other lion turtle cities. At the time people lived on lion turtle cities since it was dangerous to live on the land because spirits were their enemies. He wanted to bring balance to the world so he learned the elements. At the time people gained the power of the elements from the lion turtles such as aang did to the learn energy bending so he traveled with the light spirit to other lion cities to gain their elements and trained with the elements but he needed to light spirit to use the other elements so she pass through him which let him bend other elements eventually he fought the dark spirit he fused with the light spirit which pretty much makes the avatar state happen to beat the dark one and he sealed the dark one away so no one can let him free.And the lion turtles stop giving people the elements to use in this new era. so if someone were to get power from the lion turtles and let a spirit pass through them then they could bend all the elements im not sure if you need the dark spirit to be like the avatar but if some let out the dark spirit and got all the elements they could be like a anti avatar person like the dark avatar so that's a small of possibility of someone bending more than one element you watch the episodes 7 and 8 of season 2 to watch the story of the first avatar

As shown in the show, they got the ability to bend from lion turtles, one theoretically could bend all four elements, just not all at once, as that seems to only be possible in the avatar state.

When Avatar (Korra) allowed the Spirits to enter the physical world, people mysteriously began to gain the ability to bend air, only few had access to this power because,to have gained it,both your Parents or your Grand Parents had to be 2 Water benders, 1 air bender and 1 water bender, or 2 air benders. The energy that spread the power could go extremely far but, it didn't get as far as the water tribe, on the other side of the world (as you know they didn't search there.) but, If someone with those Genetics may have been somewhere closer at that time, they could have gained two bending abilitys.

In addition,

There is one problem with this though, the body can't handle bearing more than one element but, no worries, On an episode of The legend of Korra we met, Wans uncle, who had been possessed, this in fact made him a better bender as his body was able to handle it.
So when unalak released all the spirits whilst fighting giant Korra, someone may have been possessed making them strong enough to bear two elements.

It hasn't been seen though, and Bryke hasn't said anything so, I guess we'll never know.

No, bending is genetically passed on by DNA, sort of like a dominant gene.

Avatar Aang has 3 children, a water bender an air bender and a non bender. His air bending child only has air bending children.

This shows that children can only inherit bending from their ancestors. Excluding the Avatar, nobody can learn more than 1 bending, if they even posses the power.

No. Regardless of any proof you may find, only the Avatar can master all four Elements. Benders always had the ability, their respective animals helped them unlock it. The only person with the ability to bend every Element is the Avatar. No exceptions whatsoever.