My mind went onto two different tracks--
One, you declare your divinity as you begin your journey through this dungeon as you progress and become more powerful, things become a test of faith-- like if you're a god of slaughter, it's reasonable enough that you'll just go through rampaging over everything in sight. Except, what if you come across a peaceful town that says they'll give you an heirloom set of weapons and sacrifice a goat to you every year if you'll just go away and not kill them. Your faith would dictate that you kill them (or convert them into a berserking army, or whatnot), but you lose out on New Shinies. At any point, you can choose to ascend to official godhood, where you're put to the test by the preexisting gods and, based on how well you kept your own faith, how many followers you've picked up through your journeys, how personally powerful you are, etc. you're given bonuses and penalties.
Two, take something more endless dungeon dive with a broader skill and alignment system, except reality starts warping around you as you learn further and further away from equilibrium. Start leaning towards fire? Flame-based entities have a chance of going neutral/allied, you start becoming immune to burning and mundane sources of cold... but the world does not approve of being so unbalanced. You'll start coming across more aquatic/swampy floors where you're weakened, divine frozen monsters, walls of ice, etc. RNG spread is opened much wider, and things become much more chaotic in general, as your power starts warping normal reality. And this one didn't get nearly as much thought since it didn't seem as interesting.