Well, one way could be through some super - rare and powerful jutsu that transfers the dojutsu abilities to him. Maybe a forbidden jutsu that was long forgotten but he stumbles upon it somehow.
In some fanfictions, Naruto might obtain all dojutsu through some kind of ancient inheritance. Maybe he discovers a long - lost scroll or a hidden temple that bestows upon him these powerful eye techniques.
The balance in the ninja world would be completely disrupted. Allies might start to fear him as well. Naruto would have to be very careful about how he uses his powers to avoid causing chaos. He might also face moral dilemmas. For example, some of the dojutsu might give him abilities that could be considered unethical if misused, like mind - control - like powers. So he'd need to figure out the right way to use all these new powers.
One implication is that he would become an extremely powerful force. He could easily detect enemies, even those hidden or using stealth techniques, with the sharingan. And with the byakugan, he could have a near - perfect view of his surroundings. This would make him almost unbeatable in battles.
He could get a Dojutsu that allows him to manipulate time. This would be a very powerful ability as he could slow down or speed up time during battles. For instance, he could slow down time to dodge an enemy's attack and then speed it up to counterattack.
Well, it could make him an even more powerful ninja. The Dojutsu might give him new abilities like enhanced perception, the ability to see chakra more clearly, or even some kind of special attack. For example, if it's a Dojutsu similar to the Sharingan, he could potentially copy jutsu more easily.
One possibility is that he has the Tenseigan and the Ketsuryugan. The Tenseigan would grant him incredible power, such as the ability to control gravity. The Ketsuryugan could give him some sort of blood - related power, like the ability to manipulate his own or others' blood to some extent. This combination would make Naruto's character in the fanfiction very interesting, as he would have to learn to balance and use these two very different Dojutsu effectively.
Well, in some fanfictions, he might obtain it through a strange encounter. Maybe he stumbles upon an ancient relic during a mission that contains the power of the broken eye dojutsu and it somehow bonds with him.
He might gain enhanced perception. This could allow him to see chakra flow more clearly, similar to how the Sharingan can. So in battles, he can anticipate his opponents' moves better.