Hey there! So, Pokemon Mystery Dungeon DX had the feature of Strong Foes which had a chance to appear in particular dungeons with their own shiny chances. I thought it could be fun if PMU had these stronger foes appear in dungeons from time to time like they do in the overworld.
The difference between overworld and in-dungeon Strong Foes however would be that they have a very small recruitment chance. I believe that across all dungeons, fully evolved Pokemon should not be recruitable - and this would make Strong Foes unique in their ability to be recruited. They could also have a potential shiny chance - higher than usual as to compensate for said extremely harsh recruit rate. Their RR could even be tied to your explorer rank, with Strong Foes in late game dungeons requiring Guildmaster rank to be able to recruit them. That - or potentially tying their ability to spawn to your explorer rank - or having a prerequisite of their spawn be prior completion of the dungeon, which boosts incentive to beat multiple dungeons beyond end box rewards.
Their spawn rate could vary, and they’d be far from a guaranteed strong or shiny recruit, likely needing multiple boosts to have any sort of chance. They’d also be a challenge to defeat ideally - though not as strong as dungeon bosses I’d think. Another option would be to have them be non-aggressive until attacked, at least in earlier dungeons, to avoid newer players getting flattened out of nowhere.
An alternate reward could involve rare and unique drops such as TMs, eggs, dust or type damage-boost items (depending on how strong / what dungeon of course), a considerable amount of exp like the overworld Pokemon, etc. There’s a lot of things that can be done with this, let me know what you think!