Continuum from collaboration on homework to copying

That is why I have a rule that for each homework a group of students is selected "at random", and asked by the TA to explain what they turned in. The grade of the interrogation replaces the homework grade.

Rationale is that I really don't care (too much) if they copied from the Internet, got it in an obscure book somewhere, or worked it out in a group. I want them to understand, and this forces them to at least be somewhat familiar with the solution they hand in.

This is one of the reasons that for certain assignments I have been moving slowly away from grading homework individually to grading on completion and posting solutions and/or having students discuss answers in groups in class (that will be different from the ones they may have worked on the homework with). As vonbrand notes, the idea isn't so much for them to get the solution, but to understand the solution. If they just copy it without understanding, they may get some credit on the homework, but they'll bomb other forms of assessment that are more heavily weighted.

But if you really want to encourage collaboration while making it clear that work needs to be done individually you could specifically design the assignments around that idea. Each assignment could have collaboration-friendly questions and individual-oriented ones. The instructions could then say something to the effect of "You may / are encouraged to work with a partner on questions 1-3. Then do questions 4 and 5 on your own. If you check your work with your partner afterwards, please make corrections in a different color ink". This would codify the final two steps of the me, we, y'all, you progression in the one assignment and would still allow for them to check their work before handing it in and help them visualize missteps so they can avoid them down the road.

It really depends on the nature of the work and the established guidelines for grading that type of work. If it's a class of physicists in graduate school who are expected to find solutions to complex problems and collaboration is expected in determining the missing pieces to the puzzle, then there really can't be any serious expectation of wildly different proofs. If their collaboration failed on a problem because everyone counted on one member's interpretation, then it will be obvious that their collaboration was ineffective and none of them deserve all of the points for that question. Some members may choose not to collaborate and be better or worse for it. But, based on how you've presented this, it would seem it's just a matter of whether the answers are correct or not.