One plot idea is that Harry discovers he is an Animagus and his form is a dolphin when he is near water. His familiar is a mermaid. Together, they explore the underwater world of the wizarding world. They find an ancient underwater temple that holds a powerful magic that could be used for good or evil. Harry has to decide whether to protect it or use it to fight against the growing dark forces on land. The mermaid familiar helps him understand the complex underwater magic and politics.
One possible fanfic could be where Harry discovers he is an Animagus early on. His familiar could be a phoenix, for example. In this fanfic, the phoenix could guide Harry through difficult times, and their bond could be a source of strength against Voldemort. Harry could use his Animagus form, perhaps that of a stag like his father, to move around secretly and the phoenix familiar could provide additional protection and wisdom.
One idea could be that Harry has to figure out how to communicate with his friends while in owl form. He could use his beak to write in the dirt or something similar. Another plot could involve Harry trying to find a way to reverse the situation while also using his new owl abilities to his advantage, like flying to places he couldn't reach before.
One idea could be Harry discovers he's an Animagus early on, perhaps in his second year. He turns into a stag like his father and uses this form to explore the Forbidden Forest secretly. Another could be that he has to hide his Animagus form from the Ministry which is on high alert for unregistered Animagi.
One plot idea could be that Harry and Ginny discover they are Animagus during their time at Hogwarts and use their forms to secretly explore the Forbidden Forest. Their Animagus forms might give them an advantage in finding hidden magical creatures or ancient magic that could help in the fight against Voldemort.
One interesting story could be where Harry's animagus form is a stag, like his Patronus, and his familiar is a magical owl that can communicate complex thoughts. The owl might help Harry in his secret missions against dark wizards by acting as a spy.
One idea could be that in a hidden corner of Hogwarts, a student discovers a baby dinosaur as their familiar. Maybe it was brought through a magical portal from a prehistoric era. The student then has to keep it a secret while trying to figure out how to take care of it.
A plot could be that Harry is the only one who can transform into a giant wolf animagus, and he uses this form to hunt down Horcruxes in the most dangerous and inaccessible places. His wolf senses help him detect the dark magic of the Horcruxes more easily.
A plot could be that a Gryffindor Animagus accidentally reveals their form during a Quidditch match. This causes chaos as everyone tries to figure out who it is. It also draws the attention of the Ministry of Magic who have strict rules about unregistered Animagi. The character then has to deal with the consequences while also trying to prove they mean no harm.
One idea could be a story where a young wizard discovers a chimera familiar that has unique powers. For example, it can fly faster than a hippogriff and has the ability to breathe fire and ice simultaneously. The wizard then has to keep this a secret from the Ministry of Magic as chimeras are considered dangerous and illegal as familiars.
One idea could be exploring the familiar's backstory. For example, if Harry's owl, Hedwig, was actually a descendant of a magical owl family with a special mission. Maybe it was sent to protect Harry not just as a normal owl but with some hidden powers or knowledge.