In the books, Harry's double classes are always Gryffindor/Slytherin or Gryffindor/Hufflepuff. They're no Gryffindor/Ravenclaw classes, except for the upper year electives which combine all of the houses. I'd always assumed this was to prevent Slytherin and Hufflepuff from being paired. Most of the bullying we see comes from Malfoy, Crabbe, Goyle, and Pansy Parkinson, all of Slytherin. They like to target people like Neville, the Gryffindor-who-also-tends-Hufflepuff. Keeping the bullies away from the perceived-to-be-vulnerable Hufflepuffs makes perfect sense (and a lot of fanfic takes this dynamic as a given). From a story-telling perspective, the double classes we do see set up more interesting dynamics: Slytherins as Harry's antagonists, Hufflepuffs as foils or as people needing protection. Moreover, with Hermione in all of Harry's classes, the Ravenclaws are largely redundant.
The problem is that Hufflepuff's defining trait isn't weakness: it's hard work.
And Slytherin's isn't evil; it's ambition.
What if we have it backwards? If the Hufflepuffs and Slytherins aren't being kept apart to protect the kids? If it's to prevent them from cooperating?
Consider the other combinations: brave Gryffindor and ambitious Slytherin work together towards goals which may be dangerous or frightening: anything from an imperialist war to a civil rights movement. Pair Slytherin ambition with Ravenclaw intelligence and you could have all sorts of massive scientific or cultural endeavors (eradicating diseases, the space program...also nuclear arms races).
But if Hufflepuff and Slytherin start cooperating, ambition and hard work...
They could do just about anything.*
Re-structure the government of magical Britain. Achieve full civic equality for goblins and house elves. Abolish the Statute of Secrecy. Get the Americans to start playing Quidditch like normal wizards.
Really, the first thing any Slytherin worth the name should do is make friends in Hufflepuff--unless this Slytherin isn't very smart, in which case they should start by making friends in Ravenclaw, who will point out the obvious advantages to having friends in Hufflepuff. Good friends.
*I mean, any objective deserving the description of "ambition" will require some hard work. There is also the possibility of exploitation of the hard-working individuals by the ambitious ones, but that isn't an inevitable outcome.
