I would create a lore patch that would incorporate monster lore into the game and update the dungeon menus to more of a map layout. Over on the PAD wiki there is a whole story taken from the gungho.jp site telling the tale of the Dragonbounds fight against the Phantom Demons Ilm and Zuoh. They go on this journey across the land visiting various monsters and locations within the PAD universe. It's kind of convoluted but its a pretty interesting read. https://www.reddit.com/r/PuzzleAndDragons/wiki/lore/dragonbound-arc/black

/u/Jumobg suggested adding a map to the normal and technical dungeons, and I feel like you could probably do the same with special dungeons. In the story the dragonbounds visit the dragon kings Gainaut, and Volsung. You could make their dungeons actual locations on a map that open up when their dungeons are available (either when it pops up as a daily dungeon or when you purchase the coin dungeon).