Of course many approaches are right! In fact, many "answers" are right as well. This is a huge misconception that there is only one right path to only one right answer in a case. As long as you have a reason to believe in your answer, and it's not a randomly picked answer with no data/analysis backing it, then you will be fine.
I think of cases in terms of "drivers" and how mutually exclusive and collectively exhaustive they are. A typical "mental case" I give to new case solvers (and sometimes old timers also do this wrong) is: the population of birds in a city is falling. Why? Many start rambling into a "list of" reasons (what I call "the list mode interviewee"): air pollution, food, noise, urbanization, etc etc. But the truth is that these are factors that affect the actual driver of population, which are three: birth rate, death rate and -- many miss this one -- net migration rate.
So, all you need to really focus on are what the main "drivers" of a particular business problem are. The rest of the "Framework" will just follow from there. In a typical P&L case, the main "drivers" are obviously cost and revenue, but then you can expand out to what are the other things (the analogous to "pollution" " food" etc..) that eventually affect the two drivers? Those usually are, for revenue: price, demand (don't forget they are inter-related -- this is what is called "business sense" because you need to intuitively know that higher price may lead to lower demand especially for a "commodity" product such as rice or potatoes.. unless it's a luxury product, in which case demand may go up. See?). For costs: it could be fixed/var: labor, lease, overhead, etc etc..
Clarity of thought for many different type of cases only comes through practice and a lot of reading over a period of time. There is no shortcut.