One of the hallmarks of dwarf fortress is its emergent behavior. This allows to game to spontaneously construct stories with the player. However one of the most important elements to a good story, personal conflict, is largely missing in the game. What could be added is a new position to the current relationship status, enemy. A dwarf could have personal enemies in addition to friends and acquaintances.
This could be implemented by doing a search on dwarfish personalities and viewpoints as well as religions (in future releases) any two dwarfs with highly different viewpoints (i.e. people who like/dislike authority) could have a random chance of entering "enemy status". This could also be influenced by personality agitated, aggressive dwarfs would be more likely to form enemies and friendly dwarfs less likely.
I would like to quickly mention how this could fix "tantrum spirals" instead of having a dwarf in a tantrum spiral attack people at random, dwarfs would only attack people on their enemy list in a tantrum spiral. If dwarf A is attacked by B, A would not become unhappy but would rather be more "angry" towards B, causing a fistfight rather than a tantrum spiral.
This would be of especial interest if implemented with the nobles with a number of interesting possible applications. First someone who finds themselves the enemy of a high ranking nobel may find themselves quickly lined for the chopping or "hammering" block. If a noble angers the manager, they may not have their new gold bed delivered to their room very quickly (which should cause a great amount of resentment towards the manager and only minor reduction in overall happiness). Nobles may even be able to use their personal guard (or the new poisons) to assassinate nobles of a higher ranking.