The format will be the same, but focus only on non-profit / social enterprise / social impact cases.
Most case books have one of these.
Also refer to Bridgespan case interviews
McKinsey public cases numebrs 1 and 4 are good.
Bear in mind that a lot of the partners come from a private sector / MBB background, and social enterprises exist to make profit, so a lot of the concepts from other cases are still relevant