For me, case prep was like a golf swing – if I tried to correct too many things at once, my entire mechanics fell apart. It's important to continue to push yourself to develop no matter where you are in your case prep. But, the closer you get to interviews, the more you should focus on the one or two things that would most improve your performance. My last 4 or 5 cases, I asked my mock interviewers to give me the one piece of feedback that would have made the most difference between a good case and an exceptional one. It's the best way I found to allow myself to truly develop along a couple of key dimensions in the last stretch. Plus, you need to learn 80/20 at some point as a consultant.
I find that in an attempt to "perfect" case skills, people systematically under-prepare for fit. Instead of fitting in that Nth case(s), maybe spend that time working on your personal branding messages – what 3 or 4 things do you want your interviewers to collectively know about you once you leave the room? Instead of memorizing my "stories", I thought about the qualities that I wanted to highlight, and the examples more naturally flowed. Thinking about the "why" and the "so what" of the decisions you made and experiences you have had is as important as that second order insight on a case.
You will all learn a lot of random things about a variety of different industries and businesses through case prep. You will also likely meet some new classmates – and potential future colleagues! – along the way. All of this is interesting, if not fun! And you never know where lifelong friends can start from.