This seems kinda tough but here are some games that come to mind:

Slay the Spire 2

• 1-4 player co-op
• main gameplay is turn-based tcg-like deck builder (in multiplayer, turns are simultaneous but teamwork works best when you slow down and don’t all go at once)
• plot gets unlocked bit by bit mainly through achievements, which don’t always come from winning a run
• Strong class identities, and this is built on in multiplayer. You form your build from cards and items drafted from random selections, but the pools of available cards and items are dependent on your class.

Enter the Gungeon

• 1-2 players
• bullet hell roguelike dungeon crawler
• main story requires wins or at least deep runs for progress most of the time
• class selection defines your initial items, but your build can change a lot depending on what items you find
• the late story is highly dependent on your character selection

Sanctum / Sanctum 2

• 1-4 players
• FPS Tower Defense
• there are classes which form the basis for your build crafting, although other build crafting choices you make can kinda override that
• build crafting is a lot deeper in Sanctum 2 than Sanctum 1
• Story is told in pieces level-by-level
• its not a roguelite, but it’s a level-by-level game with lots of options for modifiers, which makes it playable in short sessions with a lot of replayability