It could lead to all sorts of wild and unexpected plot developments. Maybe Loki uses this control to manipulate Tony into doing things against his nature.
One great Loki x Tony Stark fanfic is 'The Unlikely Alliance'. It delves into a scenario where Loki and Tony are forced to work together against a common enemy. Their interactions are filled with witty banter and a slow - building understanding between the two very different characters.
In fanfiction, their friendship could start from a mutual understanding of being outcasts in a way. Tony, a genius among humans but often not fully understood, and Loki, the adopted Asgardian with his own complex identity. They might bond over their intelligence, with Loki's magic and Tony's technology being points of fascination for each other.
Maybe in a fanfiction, there is a cursed ballet. Tony Stark and Loki are both drawn to it for different reasons. Tony because of his love for all things unique and Loki because he senses dark magic. They have to team up to break the curse. During this process, Loki has to use his ballet skills (which he has been hiding) and Tony uses his tech to figure out the source of the magic. As they work together, they form an unlikely bond.
Yes, there are quite a few. You can start by looking on popular fanfiction platforms like Archive of Our Own. Some of them might explore unique relationships between a female version of Tony Stark and Loki, with different plotlines ranging from them teaming up against a common enemy to having a more romantic or complex relationship.
Maybe Loki gets stranded on Earth and Tony offers him shelter in Stark Tower. They start to have long conversations about power, responsibility, and their respective places in the universe. Eventually, they team up to fight a common enemy, like a new powerful alien threat that neither of them could face alone.
Another theme is redemption. Loki, being a character with a rather checkered past, often goes through a journey of redemption in these fanfictions, and Tony Stark sometimes plays a part in that. They might help each other become better versions of themselves.
There is also 'A Meeting of Minds: Loki and Tony'. This story delves deep into the minds of both characters. It starts with a rather hostile encounter between them but gradually, as they understand each other's motives and capabilities, they form a unique bond. It's a great exploration of their personalities.
One common theme is the power play. Loki is a powerful god and Tony Stark is a genius billionaire. When Loki makes Tony his pet, it's a shift in their normal power dynamics. Another theme is the redemption arc. Sometimes Loki uses this situation to redeem himself in some way, or Tony finds a new purpose while in this strange situation.
Their interaction would be full of tension at first. Loki is a trickster and Tony is a skeptic. Loki would likely use his charm and magic to try to throw Tony off, while Tony would be using his sarcasm and intelligence to counter Loki's advances. It would be like a clash of two very different personalities, one from the world of magic and the other from the world of science and technology.