At the core I imagine a point&click adventure, with all its elements (riddles, characters, dialogues …). Then you add direct control, some interaction with your environment, all the dynamic, options and joy a platformer can offer.
Dunno, let’s do something ordinary: You need some hay and are below a barn. There’s no visible entrance but there’s a dude inside the barn. He won’t give the hay away because he’s stuck (kids hid the ladder) and he wants to get out. You find a luke under the barn and agree, that when you find a rope, he can slide down and gives you some hay in return. Nearby you can find a rope, without luck, it appears too short and rotten to him, so, it’s time for a fab do-it-three-times-Grossman, get the ponytail from the pole dancer, the internet cable from the school and trap the giant green snake the Nickle News wrote about. One of your characters has knots powers but it won’t work until you hypnotize the snake (on hard the snake is shortsighted). Rope is done, back to the barn, give it to the dude. You need to jump and throw it at the highest point and clac his arm’s weird movements into as well (he has problems the hypnotist couldn’t fix), when things align, he grabs it, slides down and brakes his leg (he thinks, the rope still was kind of short), of course he forgot about the hay. So, you need to climb up the wall a little bit and jump at the rope at the right moment, then you can have some fun swinging around (beware the spiders, depending on your char) and climb up the rope to get your hay.
And so on. Once you start thinking about it, there are so many possibilities, you can combine in sequencial, interleaved and parallel ways (if you have the resources).
It’s just important that you get the controls right and that they’re fun (the jump&run, all the actions & selections and your inventory). The right balance between a game and its controls made some Arcades click.
Btw. Space Slime was fun because it was a nice design and the controls weren’t in your way. Once you placed the cursor on the button, you could lean back and enjoy the game.