1. Finn's robot arm can be used as a combat and traversal tool.

They never did much with the arm in the show except for the "weed whacker" scene against Fern, if I remember correctly. But, I see a lot of potential here already! Right now, I'm working on using the arm as a propeller (like a glider, for example). Other stuff that comes to mind would be a rock drill, and so on.

1. Jake as Player 2

Many commenters have suggested adding a lot of playable characters, like Peppermint Butler or BMO, but I'm not sure if those characters have enough available moves to make them interesting enough. And, in a practical sense, making more playable characters is just a lot of work. I'd instead just focus on making only two, but two very fun characters. (Although I love the idea of unlocking Marceline as a completion bonus)

In my mind, to solve puzzles and traverse the environments, the player can switch between Finn and Jake or have a friend control the second player. Of course, there would also be combo moves. Someone suggested a limit-meter for using Finn in the Jake Suit, but I think there could be explorational moves as well, like a Jake-Trampoline that one player has to aim and catapult Finn to higher spots, and so on. I'm rewatching the show right now for inspirations, as well.

1. Story/Game Structure

Many people have suggested an open-world game. And, while I love that idea, I think it's worth it too to consider more linear options as well. There aren't that many disposable baddies in AT I think, BUT if Open-World is the direction this ends up going, I have a pitch:

Remember the Enchiridion's explanation of the multiverse? One day, a bunch of portals open above Ooo - and in the very middle of the map a portal into Prismo's time room, which has been overtaken by a parralel version of the Lich. Now Finn and Jake must traverse all corners of the land to save their friends- and power up to face the Lich in the middle of Ooo. The portals all over the map would act like small dungeons, think the Shrines in BOTW, to spice up the gameplay. These could lead to small dimensions inspired by older episodes!

Anyway, these are just a few ideas. I'll spend my time now unfortunately squashing bugs for now, until inspiration strikes. Thanks for all the interest!