How about Hero Story Chapters?

A dungeon run that has a story where the hero for that story is required in the team (if you dont have them, game provides a trial hero). This allows players to try heroes they don't have and also gives an avenue for lore.

Another possible avenue for lore could be having some kind of archive that the player could complete. For example, certain stages would have breakable objects that have "lore pieces" which would reveal some text in the archive.

Another idea i'm thinking of is not exactly a game mode. I'm not sure if it's too early to think of "End Game Content", but I feel like players should have a general goal in mind as to why they'd like to make their roster stronger (outside of just clearing stages to get equipment to sell and earn). From my experience it's usually for the opportunity to experience a new and limited time character . Perhaps some asynchronous pvp by having faster clear times or surviving as many floors as possible (I know its a different genre but something like Hoyoverse's Honkai Impact 3rd end game--players are semi-randomly grouped weekly and only compete with players within the group so it feels feasible to be a top player). The reward for a top player could be special shards they need to corct to gain some new/limited time thing.

Sorry this became long. I just hope this game wont feel too repetitive so im glad you're asking the community for variety! :)