There are potentially two prongs of investigation here.  One would be changing the fundamental way that organizations are structured; this topic is explored eloquently in this cold-takes post, and I agree it seems very promising (although I don't know much about it).

Another side to "improving corporate governance" might include efforts to encourage corporate adoption of assorted management / forecasting / decisionmaking techniques at lower levels -- not fundamentally changing the shareholders/board/CEO/etc structure, but perhaps exploring things like using prediction markets in various contexts.  The benefit here would be twofold: first, by improving corporate decisionmaking, we would be spreading better management technology and marginally increasing economic growth.  Second and more importantly, corporate adoption of innovative new mechanisms (quadratic voting might also be relevant here, and I'm sure there are others), we help mature those mechanisms to the point that they become easier for other organizations including governments to start using.

Cultural values and context of any given company can be very important. For examples where there are counter-weights to profit maximization, you might find this exploration of community stakeholders that are a part of corporate culture in Japan interesting (this community-centeredness also contributes to the unique longevity of Japanese businesses). 

When it comes to thinking about board and investment incentives,  a nuance to consider is the difference between long-term profit maximization and short-term profits. Outputs of companies with long-term profit maximization seem more often aligned with social benefits than those of companies whose strategies are entirely based on quarter-to-quarter read-outs.

This is an area that I'm curious about and currently doing some independent research in - would love to connect and share thoughts. 

Maybe you wanna check Sanjay's posts on ESG and the universal ownership approach? Also FHI's report on the Windfall Clause. But if you're more concerned with governance itself from a mechanism design point of view, I remember some people dealt with it in iidm, and you could follow the Effective Institutions project (sorry, I totally should provide the links, but I still have some trouble to do it on my phone)

Maybe stating the obvious, but I believe corporate governance is an academic subdiscipline of finance/economics. From quickly looking on google scholar, here's a textbook and an (outdated) 1997 survey article. I'm not familiar with that literature, but I'd guess the normative framework (if any) taken there is the usual sort of loose willingness-to-pay-proxied quasi-utilitarianism found in most subfields of economics besides public finance.   

I'm currently evaluating the feasibility and expected value of building a proxy voting advisory firm that would make EA-aligned voting recommendations. Would love to meet with you or anyone with expertise.