Yes, but there is a subtlety to be aware of: if you use the same rubric on a subsequent assignment, the rubric and all of its comments get *copied* for the new assignment.
Here's a concrete example and the rationale:
I do song lyric analysis mini-essays to get kids to wrap their brains around decoding and interpreting text. We might do three such short papers. The rubric for each one is identical; the songs change but the objectives stay the same. The comments on papers for Song #1 will largely still be applicable for #2 and #3.
Let's say on Song #1 a lot of kids get this feedback comment: "Your thesis can't just be a summary of what the singer says."
Then on Song #2 I'm going to edit that comment to read: "We talked about this in class after Song #1, thesis can't be a summary!!!"
I still want the original comment preserved for those Song #1 papers that have already been graded. This is why the system always works with copies when a rubric has already been used in a previous assignment. Song #2 starts with an identical copy of the rubric, but it's allowed to diverge without retroactively changing what was in the rubric for Song #1.