Yes, indeed, your profile seems interesting.
Furthermore, McKinsey has a program called generation that is sort of a non-profit too. THey are focused on education, with the McK push, money and consulting-approach to things.
They employ both consultants and hire people ad-hoc for the project.
When I was in the Madrid office, they were quite big already!
It´s a very popular idea for secondments.
Hope it helps!