Have a big open world that spans across all generations. Kanto and Johto would make up the main game world and would be linked together in the main story plot. Hoenn, Sinnoh, Unova, and Kalos would each be accessible via some type of transit, like boat, plane, or train and would be unlocked via free DLC released a few months apart from each other. They would each have their own main story, but would still be slightly connected to the main story back in Kanto/Johto. There would also be plenty of side quests to optionally do.
Combat will see a major change, with you directly controlling the Pokemon in real time combat. The main buttons (a, b, y, x) will perform typical RPG functions like interact, jump, use equipped item (think fishing rod), menu, etc. But when battling, these are your Pokemon's moves (anything from their current move sets). Moves will be fueled by power points and also feature a cool down period between use. The Pokemon's speed stat is the primary factor for cool downs (and also movement speed) while priority moves will feature faster cool downs. Some moves may become more useful in the new combat, others less useful. Basically, combat will be like in the anime, only without bullshit plot convenience interfering with battles.
Many familiar RPG elements will be present, such as the new leveling up system. Defeating Pokemon will give exp to your Pokemon while completing quests, achievements, etc. will grant exp to your character. Leveling up your character will allow you to claim new trainer perks such as faster egg hatching, better shop prices, better chances at finding a shiny, better Pokemon catch rates, etc. Defeating Pokemon give you blank EV points, more depending on level, to distribute when you level up as you see fit. No more just HP EVs from grinding Audinos.
Running out of characters, but that's the bare bones of my idea. Obviously it has lots more to be fleshed out. But every Pokemon will be catchable in some way in the game.