I think that actually it's quite relevant to consider that social institutions actually are owned (in the practical sense, not in the legal one) by someone, and that it matters by whom and how they are owned.

Yes, there's the common scenario of social institutions that are owned (controlled, funded, etc) by the whole community they're serving. But there are cases also of important social institutions (for example, education) "owned" by particular subgroups of that community e.g. the various historical examples of key social functions being performed by churches, or funded by particular wealthy individuals for their community, or social institutions implemented by a foreign government/elite for the locals (both in the case of conquests and colonial empires) - in which case the ownership mattered quite a lot; because in this case the social institutions run for the local people weren't controlled by the locals and were significant instruments of political and social influence and control by the "owners" of these social institutions. Which has interesting parallels with the current megacorps controlling much of the information flow.

That would be one of the pillars. The investors. The link of obligation being the contract of ownership.

The links to the other pillars being the contract of purchase (customers) and the contract of employment (employees).

I guess social institutions have just one pillar (the customers).

This is a very interesting idea that I hadn't really considered before.

Under this system would it still be possible to fire people without cause? Would there be some mechanism to share profits with the employees? Without those I think it would still be a situation where some of the stakeholders are more "first class" than others.

I use companies like docker containers to protect assets.