5d hexcrawl with multiverse timetravel

Imagine your standard hexcrawl. That's 2D - north and south. 

But what if you've got the underdark, as in Veinscrawl? (Notably, most long-form treatments of the underdark treat it as divided into vertical region that progressively weirder the lower down you go.) Then you've got your three classic spatial dimensions, so we're up to 3D. (This also lets you throw in your cloud giant castles and what-have-you.)

Take the conceit of the more recent editions, that sideways from our world is the Feywild, where everything is more alive and vibrant, and in the other sideways is the Shadowfell. 4D! (I know what you're thinking, and to answer your question, per the 4e underdark book the intersection of the underdark and shadowfell has the supremely stupid name of the Shadowdark, not the equally stupid name of Underfell. The name of the intersection of feywild and underdark isn't funny enough for me to remember.) 

And if you have calendars, not just maps, that's 5D.  

Some additional things that you can use to play around with this:

• Time passes more quickly in Faerie. The way I'd be inclined to play it is that the Feywild has the same seasonal calendar as our world, but it's just the same year over and over, so that if you enter in September 23rd our time, and stay in the Feywild from September 25th, you'll exit into September 25th - but it might not be of the same year. (The feywild is also more full of glittering treasure hoards, and you can get the equivalent of a full night's sleep by just taking a breather there, so time spent is more valuable as well.) 
• Time passes more slowly in the Dolorous Lands. You can spend an arbitrary amount of time there and when you exit, it will be the next 4AM or so. However, you can't rest there; at least, not meaningfully.
• Especially with a good downtime system, this works for games where not everyone is going to be able to make it to every session. 
• It also might work well with a very long-term calendar, NPCs that have some branching futures (like these), some kind of domain management...

(See also.)