Another possibility is that Doctor Strange could rescue Peter. He has powerful magic and the ability to travel through different dimensions. He might sense that Peter is in danger through his magic and use his powers to find Dark Tony's lair and free Peter. Strange could also use his magic to fight off Dark Tony if he tries to stop the rescue.
One possible plot could be that Dark Tony has some sort of vendetta against Peter. Maybe he believes Peter has something that belongs to him, like a piece of technology or some secret information. So, he kidnaps Peter to get it back. He might hold Peter in a secret lair and try to force the information out of him. This could lead to a series of events where Peter tries to escape and outwit Dark Tony.
In a fanfiction sense, Tony might kidnap Peter due to a misunderstanding. For example, if Peter was involved in some sort of experiment that Tony misinterprets as dangerous. He could be worried that Peter is being influenced by the wrong people or powers, so he kidnaps him to figure out what's really going on. Tony's actions, although extreme, could be driven by his love and concern for Peter as a mentor.
One possible plot could be that Quetin Beck, with his advanced illusions, manages to deceive Peter Parker and lure him into a trap. Beck might have some vendetta against Spider - Man (Peter) for ruining his plans in the past. He could then hold Peter in a secret location, perhaps a high - tech lair he has created. Peter, of course, would be trying to figure out a way to escape using his wits and powers.
Often, they emphasize the relationship between Peter and Tony. It could be a mentor - mentee relationship like in many stories where Tony imparts his wisdom and experience to Peter. For example, in some fanfics, Tony helps Peter understand his powers better.
Perhaps in the fanfic's storyline, Tony is facing a lot of pressure himself, like threats from powerful villains or issues within the Avengers. Peter's actions, whether they are mistakes or just inconvenient timing, could be the straw that breaks the camel's back for Tony, causing him to yell at Peter.
Another possibility is a new villain who has the power to control Bucky's actions. This villain could be after Tony for his wealth or his influence in the superhero community. The villain forces Bucky to do the dirty work while staying in the shadows.
One possible plot could be that Bucky is under some sort of mind control when he kidnaps Tony. Maybe Hydra has re - activated some of his old programming. Then, as the story progresses, Bucky starts to regain his senses and realizes he has to protect Tony from other threats that emerge.
It could also be for revenge. Perhaps Stiles or someone associated with him has wronged Peter in the past within the context of the fanfiction story. So, Peter kidnaps Stiles to get back at him or those related to him. Another reason might be that Peter is being controlled by some other force. There could be a dark entity manipulating Peter's actions, and it makes him kidnap Stiles for its own sinister purposes.
Family is also a theme sometimes. They can be seen as a sort of surrogate family to each other. For example, Tony may act like a father figure to Peter. Additionally, the theme of heroism and growing into one's role as a hero is often explored. Peter is learning from Tony how to be a better hero, and Tony is also learning from Peter in some ways, like how to have more hope and innocence in the face of danger.