Karquelle

Karquelle is the poly ship between Barbie Roberts, Ken Carson and Raquelle from the Barbie fandom.

Canon
Barbie and Ken have a relatively stable relationship. This does not sit well with Barbie's long time rival Raquelle, who wants to take Ken for herself.

Barbie in A Fashion Fairytale
The movie starts with Barbie being fired from her latest fairytale movie, because she criticized the direction taken for the story, so she perks up when she sees that Ken is calling her. However, "Ken" is breaking up with her and is avoiding questions as to why. Barbie then realizes that she needs to take a vacation and decides to visit her aunt in Paris to help her with her fashion business.

Barbie's friends heard the whole thing and then see Ken talking to Raquelle the next day, so they assume that Ken dumped Barbie to be with Raquelle. When they confront him about it, Ken is confused and genuinely believes that he and Barbie are still dating, but Raquelle acts evasive. When Barbie's friends tell him what he supposedly said when he broke up with Barbie, Ken realizes that those were lines from a script Raquelle asked him to read the other day. Though Raquelle plays dumb, Ken realizes that Raquelle took the recording of the script, called Barbie on his phone while he wasn't looking and staged a break-up to have Ken all for himself. Raquelle's attempt at wooing him further fails, he is focused on getting to Paris to explain everything to Barbie. Raquelle makes no attempt to stop him.

Barbie: A Fairy Secret
The movie starts with Barbie and Ken attending the premiere of their latest movie, with Raquelle interrupting Barbie's interview to steal the spotlight.

After Raquelle rips Barbie's dress, Barbie, her friends and Ken go out for ice cream to cheer her up. However, outside the parlor, Barbie and Raquelle witness Ken being kidnapped by a lovestruck fairy, with Barbie's stylist friends revealing that they are actually fairies in disguise. Raquelle attaches herself to the group, having no interest in helping Barbie, but hoping that her saving Ken will win him over. They let her come along, but during their journey through the fairy realm, Barbie and Raquelle start growing closer. Eventually, they reach Ken, but the lovestruck Graciella freezes all of them in place, including Ken. Ken manages to reason with her to the extent that she'll merely imprison them until the wedding is over, which would mean that Ken would be stuck in the fairy realm forever. However, by affirming their friendship, Barbie and Raquelle manage to counteract Graciella's magic imprisoning them and they rush to crash the wedding. Ken is put in chains to avoid him from bailing on Graciella, but Barbie and Raquelle manage to snap her out of it, revealing to everyone that she never loved Ken, but was under the effects of a love potion. Graciella is grateful for their help, finally being allowed to be with the man she truly loves and offers to use her magic to send Barbie, Ken and Raquelle home. However, when they meet at the ice cream parlor the next day, they discover that they can't remember what happened yesterday, believing that they all shared the same strange dream. Regardless, Raquelle sits next to Barbie instead of Ken, showing that Raquelle remembers becoming friends with Barbie and respecting their relationship.

Fanon
Though the threesome between them doesn't get much content, it is a fairly well-respected solution to the Karbie vs. Barquelle conflict.

Ironically, despite Raquelle only making eyes at Ken in canon, many portray the relationship as Ken and Raquelle sharing Barbie. Raquelle is often interpreted as a closeted lesbian, who tries to hide her crush on Barbie by going after the one she desires.

Fandom

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