while I have no particular McK-experience, I have a lot of PE experience and can give you some of the most common case types we would give at Bain.
1) Acquisition - Should the client aquire the target or not?
2) Synergy - How can you atain synergies with two related PE portfolio companies?
3) Sector attractiveness - Can you evaluate the market attractiveness for market X?
4) Value creation (essentialy a profitability case) - What are the value creation levers at company X and how much do they amount to?
There are obviously a lot of other case types but these are the most common one in my opinion.
I hope this helps.