Switching Systems

The systems of Dungeons and Dragons are largely designed to work with a small group of PCs.  The systems can start to break down when used to model interactions that are outside that scope, like a huge pitched battle.  Individually tracking hp and attacks from thousands of combatants takes too long, so we have to use some other way.  The DMG has some skeletal mass combat rules, you can make up your own, or you can set up a normal dungeon/encounter structure within the larger battle.

-The PCs fight the enemy king and his honor guard, while the rest of the army battles around them, acting like terrain.
-The PCs sneak off on a special mission that requires them to sneak into the castle and open the gates, dispatching guards silently along the way.

Stuff like this is cool, fun, and works with the systems of DnD we're used to. It treats the PCs as special commandos that accomplish specific tasks.

There is another option though, one I have always wanted to try.  Use several obviously different systems to model one shared imaginary world.  As a (bad) example, let's say there is about to be a huge battle. The DM takes out a chessboard and says that the players are black, the DM is white, and whoever wins the chess game wins the battle.  The black left knight represents a favorite NPC of the players, while the white bishop is a hated foe.  So if these pieces are taken, a player can narrate a quick death scene for them, and the players might play chess differently to keep their knight alive.  Halfway through the game, they take a break and play a quick encounter with DnD rules.  If the players are smart, they can gain some advantage on the chessboard.  Then they finish the chess game with their new powers (because they found horses and gave them to that group of spearmen, this pawn moves like a knight)

Look at all these NPCs

What I like about this is that the world is understood in both systems, and can lead to weird gameplay.  Maybe the PCs just want to kill the white bishop, and then they think that they can convince the other king to make peace?  So you play chess, with a totally different aim than normal, with one side trying to kill a bishop and the other playing normally.  Then you switch to the PCs riding out to parlay under a truce flag.  Did the army kill the queen while attacking the bishop?  Maybe the king is now distraught and angry, unwilling to make peace.  Did the PCs have to sacrifice a lot of material to get the bishop?  What does that mean for the social structure of their army?

In general, I think switching systems like this could lead to a lot of emergent gameplay, with weird objectives in both games as the players try to use both systems to their advantage.  Chess is actually not a great choice here, since chess skill can vary so widely and it takes a long time.  You could use a game of Magic the Gathering with special decks representing both sides.  If your players are short on mana, they can do a little DnD encounter to get "supplies" and add one mana to their pool.  It could work with a lot of different games. What kind of situations could Love Letter model?  What if you played Werewolf but the werewolf is eating beloved NPCs?

Probably shorter games are better in general for this.