I believe the best way to train for a case interview is by trying to simulate as much as possible the actual interview environment. I experienced multiple sessions with fellow candidates by the time I was applying and also experienced multiple real-life interviews - and I can see that there is usually a huge difference between the approaches.
In a real interview, usually interviewers challenges you as much as they can. They try to take you far from the comfort zone and leverage case topics that casebooks usually do not cover. When training with partners, it is hard to avoid the casebook formula. Case partners are not used to challenge your answers as much as firm partners do.
Therefore, my approach is to try to simulate a real-life interview as much as I can. It is very important not to skip the fit part and, when it comes to the case, I try to be as challenging as a real-life interviewer will be. If we go through multiple cases, some of them will be traditional and some of them won't, for example. It is crucial for the candidate to be prepared to multiple case formats and paces - and not only the classic ones.