In a crossover with the DC universe, Superman could be an interesting character to pair with Master Chief. They are both strong and have a sense of justice, but their powers and methods are very different. Another good one could be Batman. The contrast between the high - tech Master Chief and the more detective - style Batman would make for an exciting story. In the Marvel universe, Captain America would be a great pairing. Their leadership skills and commitment to their causes could create some great interactions.
Another possibility is a crossover where Naruto is brought into the Halo universe. Naruto's chakra powers would be a very unique and powerful addition to the Halo setting. He could use his shadow clone jutsu to confuse the Covenant enemies. And perhaps Master Chief and Naruto could have a friendly sparring match to learn from each other's fighting styles.
One idea could be a crossover with the Star Wars universe. The Master Chief could find himself on a planet in the Star Wars galaxy, facing off against Sith or Jedi. Maybe he teams up with some of the Rebel forces. Another idea is a crossover with the Warhammer 40K universe, where his Spartan skills are put to the test against the various threats in that dark and gritty setting. A third idea could be a crossover with the Mass Effect universe, interacting with the different alien species and getting involved in their galactic conflicts.
One great 'Halo Master Chief Time Travel' fanfiction is 'Master Chief: Through Time'. It has an interesting plot where the Chief is sent back in time and has to deal with past Covenant threats using his future knowledge. It's a really exciting read.
One interesting plot idea could be a story where the female Master Chief has to lead a ragtag group of survivors through a Halo ring filled with new and dangerous Covenant mutations. Another could be her facing off against a rogue Spartan who has turned against the UNSC. Or perhaps a story where she discovers an ancient Forerunner technology that gives her unique abilities, but also attracts the attention of a powerful enemy.
One possible storyline could be them teaming up against a new, powerful alien threat that neither the UNSC nor the Covenant can face alone. They have to put aside their differences and combine their unique skills and knowledge. Master Chief's combat expertise and the Female Arbiter's understanding of Covenant politics and technology would make for an exciting partnership.
Perhaps a plot where the Covenant discovers the Naruto world and wants to harvest the chakra as a new source of energy. Master Chief, being the hero he is, travels to the Naruto world to stop them. Along the way, he meets Naruto, who is initially skeptical of this strange armored man. But as they face the Covenant together, they learn to trust and rely on each other. Naruto's ability to adapt and Master Chief's combat experience make them a formidable team against the Covenant invaders.
A third common theme is self - discovery for Master Chief. When he travels through time, he often has to re - evaluate who he is and what his purpose is. He may see different versions of himself or be in situations that make him question his own beliefs and values. This adds a deeper, more psychological layer to the usually action - packed Halo stories.
The Arbiter could be a great character to pair with the female Master Chief. Their different cultures and combat styles could create an interesting dynamic. Another good option could be a young UNSC engineer. The contrast between her combat skills and the engineer's technical know - how could lead to some great story moments. Also, a fellow Spartan, maybe one with a more light - hearted personality, could be paired with her for some buddy - cop - like adventures in the Halo universe.
For Master Chief, his character could be developed by showing his reaction to working with a former enemy like the Female Arbiter. We could see his internal struggle as he has to trust someone from the Covenant. For the Female Arbiter, her character can be developed by exploring her view of humans through her interactions with Master Chief.