I think the most logical choice for you is most certainly a top MBA program.
One of the absolute best options in the world would be Stanford Business School’s MBA program. They have an extremely well regarded centre for social innovation and many coursework options on social impact orientated start-ups and corporates that help train future leaders interested in this space.
Having participated in a top management consulting firm (I’m hoping Bain, McKinsey, BCG, Oliver Wyman etc or at a second tier Strategy&, Deloitte, Booz Allen etc), there’s little value in going back to university and studying at a program that isn’t globally ranked and reputable (Global Top 30 MBA, US Top 20, UK Top 10, Australia Top 2) kind of thing.
Go to a top business school where you will be surrounded by many sharp minds who typically have a deep socially driven purpose who can challenge your thinking in the presence of amazing professors (Stanford Business School basically only takes people with a very strong social element to their candidacy so the intimate class is carefully screened to have some interest in this).
There are some more fringe programs like this: https://www.jbs.cam.ac.uk/programmes/professional-practice/mst-social-innovation/
This is designed for people with more professional experience than you, however, typically later in their careers.
I would also consider going for a PhD in the field of social innovation if you are fascinated by it as research into this space is still undersaturated.