Cain and Abel and Seth

In this trope, a third person is introduced specifically in a way to complicate the relationship between established siblings, or between the established siblings and the new sibling. If the characters aren't related by blood, but through the same Meta Origin consider themselves Blood Brothers or Bash Brothers literally, then another character with the same Meta Origin and honorary sibling status may suffice.

Consider the trope namers. Many people know the story of Cain and Abel, the first children born in the Abrahamic religions. As You Know, Cain kills Abel, and was banished by God. What fewer people know, is that Adam and/or Eve had several more kids, only one of whom was named, Seth. Seth would replace Abel as the "good" son, and while both he and Cain would have children (with their unnamed sisters), Cain's lineage would be cursed, and would eventually all be doomed by the Great Flood. Noah and his family were descended from Seth, and as the only survivors of the Flood, this means that all humans are descended from Seth, taking both of their places as the future of humanity.

Considering these characters can be introduced quite some time after the original set, spoilers may be ahead.

Compare Long Lost Sibling, which can possibly be a supertrope to this, Cousin Oliver, Remember the New Guy? and Tangled Family Tree.

Examples of Cain and Abel and Seth include:

Anime and Manga

The late introduction of Shizuku in Candy Boy, with her Big Sister Worship of Yukino and slight Sibling Rivalry with Kanade, really shakes up the twins' dynamic.
In One Piece, Luffy and Ace are revealed to not be related, and have a third Blood Brothers named Sabo. In their youth, he was the physical midpoint of the three, and was The Spock in their three man band. The story is told entirely through flashback, as Sabo is assumed dead and thus a Posthumous Character. His death, and Ace's subsequent death, To the viewers, this complicates every previous interaction between Luffy and Ace, their current situation, and all those that would follow. Additionally, Ace's tattoo and Luffy and Ace's relationships with their True Companions take new significance. In a cover, it is shown that had Sabo lived, the three would be together, and to cement this "Good Future", Ace's tattoo loses its meaningful misspelling.

Comic Books

In X-Men, a slip up by Mr. Sinister introduced an example. As explained on the Tangled Family Tree page, Scott Summers was introduced as an orphan, then met and established a relationship with his brother Alex. This lasted for quite some time, before Sinister hinted that there was at least one more brother out there. After a lot of plot changes and Word of God statements, the brother was set as Vulcan, a supervillain emperor.

Live-Action TV

In Supernatural, Sam and Dean have spent most of their twenty-some years with only each other as dependable family. Eventually, in the episode entitled "Jumping the Shark" including references to Cousin Oliver, they find out that their father had a child several years after their mother died, whom he kept from the hunter's life to protect him. The brothers immediately argue about whether to train him or to spare him from their life. It turns out he's already been killed in revenge against their father, and they've been dealing with a ghoul.
- When Adam eventually makes another appearance in season five as himself, after he's been brought back from the dead as bait or a possible alternative for Michael, he doesn't get along with either of the brothers that never knew about him. In Season six, when Dean's given the option to either save Sam's soul from eternal torment in Lucifer's cage or rescue Adam's from the same place, Dean unsurprisingly doesn't even hesitate in choosing Sam.
- Simultaneously, within the archangels, Lucifer and Michael are seeking the same Armageddon, each thinking they would win. Winchester brother intervention gets Gabriel involved, introducing this dynamic between them to the viewers. Gabriel takes neither side, choosing humans instead, and is responsible for telling Sam and Dean how to seal the both of them in Lucifer's Cage, preventing the conflict that would raze the world.
Charmed revolved around three sisters, the Charmed Ones. One of the sisters died early in the show, so a half-sister was added down the line to complete the trio. The two elder sisters (Piper and Phoebe) tried to enlist the help of the new sister (Paige), who was reluctant to join them and almost joined the Dark Side. There were also episodes which focused on how Paige's personality affected the dynamics within the family (namely, an episode where Paige tries to rearrange everything in the house which causes tension between her and Piper). Paige was also far more emotional on decisions concerning the past of their grandparents.
The show Sisters originally had 4 sisters: Alex, Teddy, Georgie and Frankie. In the 4th season they discover they have a younger half-sister named Charley who was born from an affair their father had. Charley was a guest star in seasons 4 and 5 but when the actress who played Frankie left the show Charley (now with a different actress) became a regular character during the sixth season.
Venus de Milo of the short lived Ninja Turtles the Next Mutation series was a female turtle with the same Meta Origin. But she got so much hate from the fans and creators of the original series, and the show got terrible ratings and was cancelled, so the whole thing is noncanonical now.
Gossip Girl, where Chuck becomes Serena and Eric's adoptive brother when their parents are married. The siblings already knew Chuck, and because of his earlier attempt to rape Serena, neither of them trust him. While Eric is the first to come closer to Chuck, Serena still distrusts him and blames him for sending her porn magazines. Though, as it turns out, they were sent by someone else. Their relationship gets even worse when Chuck's father dies.

Video Games

In Mortal Kombat Armageddon Rain's Ending it is revealed he is the third son of Argus - the other two being rivals Dagon and Taven

Western Animation

In The Venture Bros, Dermott Fictel is introduced, and almost instantly separates Dean and Hank, as he is more similar to Hank, following the brothers' Divergent Character Evolution. He's hinted as being Brock Samson's son, but he is actually Rusty's accidental child, thus making him the third Venture brother, and strangely enough the only brother with a confirmed mother.