One idea could be to explore how Hercules' incredible strength affects the Fate universe. Maybe he is summoned as a Servant in a Grail War and his brute force challenges the traditional battle strategies of other Servants. His Twelve Labors could also be incorporated in some way, like each Labor being a trial he has to face within the context of the Fate story.
A third idea is a crossover where the characters from both universes have to team up to face a common enemy. Maybe an ancient evil that threatens both the world of Fate and the DxD world. They would need to combine their powers and strategies, like the devils using their demonic powers along with the Servants' unique abilities.
One great 'Fate Servant Crossover Fanfiction' is 'Fate/Grand Order and the World of Harry Potter'. It combines the magic of the Harry Potter universe with the unique Servants from Fate. The story often has interesting battles where Servants use their powers in the Hogwarts setting. Another one could be the crossovers with the Naruto world. Here, Servants might face off against ninja techniques, creating a whole new dynamic of power clashes.
Another concept is a more comical crossover. Shirou tries to adapt to the different rules and magic in the Fate Apocrypha world. He constantly gets into funny situations as he misunderstands the local customs and magic systems. For example, he tries to cook using Apocrypha - style magic ingredients and chaos ensues.
Archer from the Fate/stay night series is often a popular choice for crossovers. His cool and somewhat aloof personality can create interesting interactions with other servants.
The exploration of Gilgamesh's character is also a major theme. Many fanfictions use the crossover concept to dig deeper into his personality. They might show a softer side of him that was not fully explored in the original Fate series, or they might further emphasize his pride and arrogance in new and different situations, like when he's in a world full of magic users who don't recognize his kingly status immediately.
The cultural contrast is another aspect. Spartacus comes from a very different historical and cultural background compared to the various characters in the Fate series. This contrast can be used to explore themes like class struggle, morality, and the meaning of heroism in a fresh and exciting way. For instance, how Spartacus views the 'heroic' deeds of some Fate characters who might be from a more aristocratic background.
Well, cultural clashes are also a common theme. When Fate Apocrypha crosses over with another series, say from a different country or with a very different cultural background, there are interesting cultural exchanges and clashes. For instance, if it crosses over with a historical or myth - based series, the different interpretations of the same myths or historical events can be explored. And of course, the theme of survival is often there. Characters have to find ways to survive in the new and often dangerous situations created by the crossover.
Another theme is power dynamics. Achilles is extremely powerful, and in these crossovers, how his power stacks up against the powers in the Fate universe is often explored. For instance, his invulnerability and his combat skills are pitted against the various magical abilities and combat techniques of the Fate Servants. It makes for some really intense battle scenarios where the balance of power is constantly shifting.