quoting a previous post I wrote, the answer depends on whether the second round is the final – the one with the partners – or just an intermediary step. In case it is an intermediary step, you will go through an interview similar to the one in the first round, that is, covering:
- Introduction: are you able to summarize the information and clarify the goal?
- Structure: can you present an appropriate structure for the case?
- Graph analysis (not always present at BCG): can you interpret tables/graphs and provide insides on them?
- Math: are you able to go through a math exercise under pressure, structuring it?
- Sum up: are you able to provide a concise recommendation for the CEO/client?
The main difference you will find in a final round with partners is that at that stage they (i) spend more time on fit questions and (ii) may not have a “proper” structured case to present – during my final at BCG I had one interview which was made by two market sizing questions and a brainteaser, without any business case. That's because at the final they know you can structure and crack a case (you passed 1 or 2 rounds already) and are more interested in your logic, personality and fit with the company.