Block puzzles! You can push them and pull them and make them fall down in a not so realistic way. Some blocks might be too big for one person to move, so you’ll need to have both characters cooperate to push or pull it.
I agree that this might not be the most original mechanic, but I still wanted to put it in for the cooperation aspect.
He (Darwin) pointed at how in numberless animal societies, the struggle between separate individuals for the means of existence disappears, how struggle is replaced by cooperation, and how that substitution results in the development of intellectual and moral faculties which secure to the species the best conditions for survival. He intimated that in such cases the fittest are not the physically strongest, nor the cunningest, but those who learn to combine so as to mutually support each other, strong and weak alike, for the welfare of the community.
Mutual Aid; A Factor of Evolution : Peter Kropotkin
Paraphrasing ‘The Descent of Man’ Charles Darwin
Despite the terrible ending of the Triwizard Tournament of 1994-95, the objective to “promote international cooperation” was fulfilled. The Hufflepuff house felt their loss in full, but Jane Shepherd, a 7th year Puff, met her future husband from Beauxbatons that year. There has never been and never will be a Hufflepuff wedding with as many tears and laughter as that one.