“Exxon Mobil needs to reconnect with the forward-looking and entrepreneurial vision of my great-grandfather,” Neva Rockefeller Goodwin, a Tufts University economist, said in a statement to reporters.

Image Neva Rockefeller Goodwin and Peter ONeill, descendants of John D. Rockefeller, are among those who want Exxon to shift priorities. Shareholders will vote Wednesday on four resolutions. Credit... Brendan McDermid/Reuters

“The truth is that Exxon Mobil is profiting in the short term from investments and decisions made many years ago, and by focusing on a narrow path that ignores the rapidly shifting energy landscape around the world,” she added.

The resolution on Exxon’s chairmanship was offered for several years before the Rockefellers became publicly involved and last year was supported by 40 percent of shareholders who voted. Royal Dutch Shell and BP already separate the positions of chairman and chief executive, as do many other companies.

“You need a board asking the tough questions,” Peter O’Neill, a private equity investor and great-great-grandson of John D. Rockefeller, said in an interview. “We expect the company to figure out how in this changing world to adjust.”

Kenneth P. Cohen, vice president for public affairs at Exxon, said the shareholders pushing the resolutions were “starting from a false premise.” He added that the company was already concerned about “how to provide the world the energy it needs while at the same time reducing fossil fuel use and greenhouse gas emissions.”

Fifteen members of the family are sponsoring or co-sponsoring the four resolutions, but it appears that some have much more solid support in the sprawling family than others.

Mr. O’Neill said that 73 out of 78 adult descendants of John D. Rockefeller were supporting the family effort to divide the chief executive and chairman positions. The goal of that resolution is to improve the management of the company, which could strengthen its environmental policies and improve more traditional pursuits like exploring more aggressively for new oil reserves.