Some members of the Rockefeller family will throw their weight behind a longstanding resolution to force Exxon to change how it does business, at a time when concerns over climate change are causing boardroom rethinks across the Fortune 500.

The last two years, corporate activist Robert Monks has tried to get Exxon to split its chairman and chief executive into separate roles, in order to give the board “independent” direction. The resolutions have failed—but, just as relevant since they’re largely symbolic, they have gradually garnered more support. This year, with the backing of the Rockefellers, Mr. Monks thinks the resolution could pass.

The shareholder resolutions take aim at a variety of companies such as Citigroup, Ford, General Motors, Southwest Airlines, Southern Company, and Kroger.

But for every thrust, there’s a counter-attack.  The Free Enterprise Action Fund sues companies it thinks are “caving in” to global warming concerns and threatening profits and shareholder value.