One of the challenging parts of managing a city (I know firsthand) is animal control. 

The City of Coronado, CA has partnered with a non-profit to better manage and care for the animals in the community, without relying on euthenasia. And they've done so at lower costs and freeing up police resources that were previously tied up with these issues. While not a classic P3, this certainly demonstrates the power of partnership between government and a non-profit organization to offer better citizen services a lower costs.