You're struggling because a specific structure doesn't exist for a public case, just like it doesn't exist for an oil & gas case or a retail case.
Think of public/NGO cases as industries, not case types! So, figure out what type of case it is from the prompt (Vlad provides some good examples), and then the lens through which you qualify your framework will be NGO (i.e. cost breakdowns, difficulties, etc.).
A public case could be operations, market entry, profitability, etc. etc. Always clarify the organisation's main objective as it adds to the generally "pure profit" lens through which most other industries would be viewed. However, don't forget, efficiency/profitability still matters (in that running the NGO well means it can meet its objectives better)