Here is my view. From your question, I believe you still need to understand how to think about strategic business issues. PE cases are completely identical to all other strategic issues, and hence I believe it is completely senseless to ask for specific "frameworks" (the same is true for "market entry frameworks", "product launch frameworks" and all the other nonsense stuff that is floating around). As an MBB consultant, you also would not use a "framework" in real life! You just need to understand the core of the problem.
If the question is whether a PE company should acquire a target, then, in essence, the fair price of the target (assuming that you keep running the company) is its stand alone value (current operational profits) PLUS synergies & optimization that can be expected over a certain investment horizon. Discounting is almost always disregarded in case interviews (however you should mention it). So you need to check whether the additional value that can be created in the future will be enough to justify the price that has to be paid today (via the future resell price, since this is how PE firms make money).
The interesting thing is that this principle thinking frame is not only true for PE or M&A situations, but for 90% of all strategic decision cases that you will ever encounter (market entry, new product, capacity expansion, licence purchase, etc. etc.). It is always about value creation! If you learn to rigorously start your thinking from the principles of value creation, the typical case frameworks from well-known books like Case in Point etc. become practically obsolete, while at the same time your thinking becomes way more rigorous and mature.
Then for the structuring, there are a couple of simple notions that you need to adhere to in order to effectively set up and navigate strategic cases (for example, contrary to what is taught in the popular books, NEVER start with qualitative questions like "first I would like to understand the market context..." - this is exactly how you should NOT work as a consultan! This would be the definition of "boiling the ocean" ;-))