It's been stated how few the spots are at these firms. There are literally only a handful at some of the smaller regional offices.
So this is what you should expect to position yourself optimally to nail the final round:
1. The second round case interviews will be more in-depth and complex in testing your business sense. The structure or framework that you use to attack the problem will have to incorporate more concepts exhaustively - being MECE will be more difficult, as the case will not be straightforwardly a declining profits, increasing cost, or merger strategy case.
2. Since the second round interviews are longer, there is more room for error in how you set up your initial plan of attack. For example, if you get a market sizing question, there will be several ways to answer it, and having the right approach is essential to doing well. These are not cut and dry the same as the Case in Point examples, as you want to essentially replicate or refine upon the market sizing approach the consultant used in his/her actual work.
3. The people interviewing you will be more senior at the firm - you are guaranteed to meet with at least one manager or partner. The more senior people will have insight on the continuity of certain people they want to hire. So, utilize the resources the firms provide you - they often give you an alumni contact or interview buddy who will go over mock interviews. They will emphasize to you the core competencies the particular firm is looking for. Thus, it's essential that you not only hit home those points, but also convey an understanding of how McKinsey is different from Bain/BCG, and vice versa.
4. Nailing the behavioral part of the interview becomes even more important in the final round. The firm is potentially hiring you as a full time employee, as the conversion ratio from internships to a FT offer is incredibly high - from 90 to 100% according to office and year. So, you need to get along with the interviewers on a more personal and conversational level.