Perhaps Mew and Mewtwo are in a fight against an evil force that threatens the Pokémon world. Ash arrives at the scene and manages to communicate with them. He offers his help and through their combined efforts, they defeat the evil. As a result, Mew and Mewtwo see Ash as a true hero and allow him to catch them, leading to a new chapter in Ash's Pokémon journey.
The plot could involve Ash hearing rumors about Mewtwo's location. He sets out on a journey to find it. Once he does, he tries to communicate with Mewtwo. Mewtwo initially resists but Ash's pure intentions start to sway it.
There's a fanfic where Ash catches Mew and Mewtwo during a special tournament. The story focuses on how Ash has to face off against powerful trainers who also have their eyes on Mew and Mewtwo. It's a great read as it shows Ash's growth as a trainer and how he strategizes to keep these two Pokémon safe from those who might misuse their power.
In this kind of fanfiction, one possible scenario is that Ash forms a special bond with Mew. Mew, being the mythical and playful Pokemon, could lead Ash on an adventure full of surprises. Maybe it shows Ash some hidden powers within Pokemon that he never knew before. This could help him in his battles and his journey to become a Pokemon master.
Well, in this fanfiction, Naruto might initially approach Mewtwo with his usual enthusiasm and friendly nature. Since Mewtwo is a very powerful Pokémon, Naruto could see it as a new kind of challenge. He could try to form an alliance with Mewtwo, thinking that together they could achieve great things. Naruto might offer Mewtwo his friendship and loyalty, which could be a new concept for Mewtwo as it has often been a loner.
One possible scenario in this fanfiction could be that Ash encounters Mewtwo in a new, uncharted region. Mewtwo, being intrigued by Ash's unwavering spirit, decides to test him. Ash passes the tests with the help of his Pikachu and other Pokemon. This leads to Mewtwo seeing Ash as a worthy trainer and allowing itself to be caught. It would be a great twist on the usual Pokemon-catching storylines.
Perhaps in this fanfiction, Ash discovers that he has a deeper connection to Mew than he ever thought. It could involve Mew choosing Ash as a special trainer to carry out a very important mission in the Pokémon world, such as saving a certain region from a new and powerful threat. This would lead Ash to face many challenges and grow in ways he hasn't before.
Maybe Ash discovers Yveltal in a damaged state due to some evil team's actions. He decides to help it and in the process, forms a bond with Yveltal. Eventually, Yveltal allows Ash to catch it.
Well, the plot could be as simple as Ash coming across a wild Dragonite that is injured. He helps it recover, and during the process, a bond forms between them. Eventually, Dragonite decides to join Ash's team. It's a classic 'help and befriend' kind of plot.
In some versions of the 'ash catches mew fanfic', Ash might have a special encounter with a legendary Pokémon trainer who gives him a rare item or some advice on how to catch Mew. This encounter could be the turning point in his quest. And sometimes, Mew itself may be in a situation where it's more vulnerable, which gives Ash the opportunity to attempt the catch.
One possible plot could be that in a world filled with dark forces threatening all Pokémon, Ash discovers a way to save Mew who holds the key to restoring balance. Ash, being the selfless hero, decides to sacrifice himself to protect Mew from an oncoming, unstoppable attack. This act of sacrifice then becomes a legend among Pokémon trainers, inspiring others to be brave and selfless.