Tips for second round interviews
First of all, congratulations for making it to the second round! This is fantastic news :)
First and second round interviews are similar in format and difficulty. However, your first round interviewers will usually be more junior than your second round ones. Associates (2+ years of experience) or Engagement Managers (4+ years of experience) usually lead first round interviews while the second round is led by Partners (10+ years of experience). Partners are sometimes a little bit less structured than more junior consultants so you should try to remain flexible on the day of your interviews.
Another important tip is to reflect on the feedback that you have been given after your 1st round. Your 2nd round interviewer will usually have access to that feedback and test you on the points raised. For instance, if your feedback was to use a more structured framework at the beginning of the case then this is something your second round interviewers will test in the interviews they do with you.