One idea could be that the reincarnated character has knowledge of future events in the Danmachi world. For example, they know about certain monsters' weaknesses or hidden treasures. This could give them an edge as they navigate the dungeon. Another could be that they are reincarnated as a non - human race in the Danmachi world, like a spirit or a dwarf, and they have to deal with the different cultural and physical aspects of that race. A third idea is that the character reincarnates with a special ability that doesn't exist in the normal Danmachi world, like the power to control time on a small scale, which would completely change their adventures in the dungeon.
If a character is reincarnated into the Danmachi world, their personality could change due to the new environment. For example, if they were a shy person in their previous life, but in Danmachi, they find that being bold is necessary to survive in the dungeon. So they gradually become more assertive. Also, the new relationships they form in the Danmachi world can influence their personality. If they join a Familia with very outgoing members, they might become more extroverted over time.
One of the great Danmachi fanfics is 'A Different Perspective'. It offers a fresh take on the characters and their relationships within the Danmachi universe. The story delves deeper into the backstories of some minor characters and makes them more significant. Another good one is 'The Unseen Adventures'. It takes the characters on new quests that are not in the original story, adding more excitement and mystery.
The Danmachi light novel is finished. The author completed the series, providing a satisfying conclusion to the adventures and developments of the characters.